Thank you God, for reminding me that YOU are the source of truth. NOT online translation engines.
I went back to look at the "names" of the months in the Tanakh, in the original Hebrew, and discovered what they really are. So below are the corrected "names" - for the ordinal designations for the months of the year, with the scripture references from the Tanakh right under it..
the following information was based upon my own research when I was learning about the pagan festival to worship Ishtar (also known as "Easter" the "Queen of Heaven" and by many different names in many cultures, the demon-"goddess" offering the false promises of "fertility", childbearing help, etc).
Tamuz is also spelled Tammuz and is mentioned as part of pagan worship being done by some Israelite women in The Temple gateway/doorway in Ezekiel 8:14 (Amplified Bible, New Living Translation Bible, Message Bible). Tamuz is a Babylonian demon-"god". He is both Ishtar's son (from her own womb) and grandson (through marriage to her older son Baal /Nimrod who is the father of Tamuz.) Tamuz is the one worshiped as born on December 25, evergreen tree is "sacred to him", because when he was killed by a wild boar some of his blood sprinkled onto a evergreen tree stump and overnight it had grown into a full tree. 40 days of mourning for Tamuz's death annually. (These were all being celebrated hundreds or thousands of years before Yeshua walked the earth as man who was born, lived and died, resurrected and ascended.)
בחדש הרביעי BaChodesh HaReviyi is the Hebrew "name" for this month: translated in our English Bibles as "the fourth month". A better Translation would be "The Fourth Month" (of the year), since it's the specific designation for this month.
in Rabbinic (Jewish) tradition Tamuz has become the 10th month of the year.
This is my first year keeping track of time on God's calendar, and this is one of the months in the Jewish Rabbinic tradition that retains a pagan god's name. (Just as "our" days of the week and months of the year are from pagan gods' names.)
I will honor Yehuah this month with the Bibilical, Hebrew "ordinal name" instead of the demon-"god's" name.
this is the information I found in researching the whole year
Rabbinic Tradition calendar begins the year in September/October and calls the month Tishri. This name is borrowed from the Babylonians after the exile in 586 BCE. When many of the Hebrew "names" of the months were replaced by the Babylonian names. I could not find demon/god references for ALL the names of the Jewish Rabbinic tradition month names. So I don't have a problem with their being "named". (I might become further enlightened at some point. God is growing me, a work in progress.)
God says (Exodus 12) the year begins at the new moon nearest the Spring Equinox. And the first festival of the year is Pesach. The Hebrew months are ordinals, as are the Hebrew days of the week. (First, Second, Third, ec.) (This month is now called Nisan, by the Rabbinic tradition calendar, and is no longer recognized by Rabbinic tradition as the first month, nor the beginning of the year).
these are from my notes:
Nehemiah writes, "Thus I cleansed them [the Israelites] of everything pagan." Nehemiah 13:30
These Babylonia names of the months are NOT part of the Torah (first 5 books of the Bible), They begin to appear in the Prophets and Writings. (Nevi'im and Ketuvim)
In The Head/ Beginning Month בחדש הראשון
Nisan (Nissan) ניסן
is mentioned as the name of a month in Nehemiah 2:1 CJB, AMP, NIV, NLT, NASB, CEV. Esther 3:7 CJB, NIV, CEV, NASB, AMP. Esther 3:12 CEV
the Name is attributed to the Babylonians but it is related to the Hebrew ניצן nitzan: "bud"
*1 Hebrew nîsān, from Akkadian nisānu, the first month in the Babylonian calendar (corresponding to parts of March and April), from Sumerian nisag, first fruits : nig, ni, thing, nominalizing pref. + sag, head, top, first
aka Aviv/Abib "spring". (Canaaite names) Ex 13:4; 23:15; 34:18; Dt 16:1
Abib=ripened barley Ex. 9:31 and Lev. 2:14, and since March-April IS the season of the barley harvest in Israel
In The Second Month בחדש השני
I Kings 6:1
in Hebrew means "to illustrate" לאייר
Ziv is the Canaaite name listed for this month in 1 Kgs 6:1,37
In The Third Month בחדש השלישי
listed as the name of a month in Esther 8:9 CJB AMP, NIV, CEV, NASB
In Hebrew it's a noun: Sion
In The Fourth Month בחדש הרביעי
Tammuz is NOT listed in the Bible as the month, but is referenced as being worshipped in Ezekiel 8:14
In The Fifth Month בחדש החמישי
It is NOT listed as the name of a month in the Bible.
This Hebrew word means father, parent, sire, ancestor, progenitor; patriarch; god; head, leader, chief; origin, source; great
In The Sixth Month בחדש השישי
Is listed as the name of a monoth in the CJB, NIV Nehemiah 6:15
In The Seventh Month בחדש השביעי
is NOT lsited as the name of a month in the Bible
לשרות This Hebrew word means to soak, immerse; rest, dwell; prevail
Ethannim is a Canaaite name for this month in 1 Kgs 8:2
In The Eighth Month בחדש השמיני
Cheshvan (Heshvan) חשון also חשוון
is NOT listed as the name of a month in Bible
Bul is the Canaaite name for this month in i Kgs 6:38
In The Ninth Month בחדש התְּשִׁעִי
Kislev (Chislev) כסלו
listed as the name of a month is the CJB,NIV/NLT in Nehemiah 1:1; and in the CJB,NIV in Zechariah 7:1
In The Tenth Month בחדש העשירי
Tevet (Teveth) טבת
is listed as the name of a month in the CJB in Esther 2:16 as Tevet
In The Eleventh Month בחדש העַשְׁתֵי עָשָׂר
Shebat is listed as the name of the month in Zechariah 1:7 NIV, AMP, CEV, NASB
This Hebrew word means tribe, clan, phylon also rod, stick
In The Twelvth Month בחדש השְׁנַיִם עָשָׂר
This Hebrew word means maple, a type of hardwood tree which grows in northern regions and is cultivated for its wood and sap; hard and light-colored wood from the maple tree; sweet flavor made from the sap of the sugar maple
It is listed as a month in: Ezra 6:15 CJB, NIV, AMP, CEV, NASB; Esther 3:7,13; 9:1,15,21. CEV 8:11. CJB 8:12. CEV 9:16. NIV AMP NASB 8:12; 9:17,19 CJB 9:1,15,17-19,21
It is listed as a location in: CJB Numbers 34:4, Joshua 15:3, 16:5, 18:13,
It is named as a person in CJB I Chron 8:3
for additional information: quotes from other sources:
**2 Gen 1:14 that the lights in the heavens are for festivals and years? Neither Wayiqra/Lev. 23:10 nor Devarim/Deut. 16:9 provides a direct statement that the wave sheaf offering determines the first month.
Ezra 6:15 and Nehemiah 6:15 tie in with Beresheet/Gen 1:14 to give the biblical and archaeological evidence that together show explicit evidence that Beresheet/Gen 1:14 involves the vernal equinox so that the first month begins on or after the vernal equinox. The Hebrew word TKUFAH can mean equinox, or solstice depending on context.
Philo of Alexandria explains Beresheet/Gen 1:14 and Shemot/Ex 12:2  without the use of barley, and with the use of the vernal equinox.
Also, AVIV means SPRING, or SPRINGING FORTH, not just barley, as seen in such translations as Stone’s Edition, or even in Strong’s concordance...
The Hebrew noun TKUFAH has an inner stem in common with the Hebrew verb NAHKAHF which occurs 19 times in the Bible. The latter means "to surround" 11 times - I Ki 7:24; II Ki 6:14; 11:8; II Chr 4:3; 23:7; Job 19:6; Ps 17:9; 22:16; 88:17; Isa 15:8; Lam 3:5. It means "to go around" four times - Josh 6:3, 11; Ps 48:12; Isa 29:1 ("add year to year, let feasts 'go around'"). It means "to destroy" twice - Job 19:26; Isa 10:34. It means "to curve" once - Lev 19:27. It means "to finish" once - Job 1:5. The overall flavor of this word indicates the idea of encirclement which does not have any implication about accurate clock time measurement. The relationship between TKUFAH and NAHKAHF indicates that encirclement of heavenly bodies provides the basis of the meaning rather than the Latin meaning of equinox (equal night with day). When the word equinox is used, its original Latin meaning is discarded, and instead, the time of its practical determination anciently is meant. This time agrees with the modern astronomer's
time for the equinox although the modern astronomer uses a technical definition that ancient peoples could not have used.
...The Vernal Equinox and Ex 12:2 Gen 1:14 mentions the lights in the heavens, and these are the sun, the moon, the stars, the planets, and comets.
The cycles of the planets and comets are much too irregular in comparison to repeatable phenomena on the earth to consider in relation to a biblical calendar when considering the lights in the heavens. The stars must be excluded because during every 1000 tropical years the time of the appearance of the stars slowly shifts about 14.1 days further into the tropical year thus losing touch with the earth's seasons; this is called precession of the equinoxes in books on astronomy. Only the sun and moon remain to be considered.
The moon determines the months, but not which month is the first. Only the sun remains to be considered. The only repeatable time points involving the sun are the two equinoxes and the two solstices. Considering that the barley and wheat in Yisrael are harvested in the spring, the vernal equinox is the only logical candidate to consider that involves the lights in the heavens on the direct basis on Gen 1:14.
...the sun's shadow on a vertical object from sunrise to sunset fall exactly east-west only on the days of the equinoxes. So it is clear that Moses knew how to determine the days of the equinoxes.
When one considers that Gen.1:14 points to the lights in the heavens to determine the festivals and knowing that only the vernal equinox is related to the time of the year under consideration, Moses would naturally think of the vernal equinox in relation to Ex 12:2. That would be Egyptian training, Egyptian thinking, Egyptian context, and in harmony with Beresheet/Gen 1:14, the only explicit Scripture that directly addresses the determination of the festivals. Would Moses think of the vernal equinox if it had not yet occurred by that day? No, it would be premature for him to think of it. The natural thinking from Ex 12:2 in the context of Egypt and what Moses knew would point to the vernal equinox as having occurred. Would Moses think it was necessary for him to explicitly mention the vernal equinox in the context of Gen 1:14? If this is the only choice there was, he need not think it was necessary. Moses HAD NO TRAINING IN BAREY HUNTING OR ITS DETECTION! THE TERM “THIS MONTH” WAS A MONTH BASED ON EGYPTIAN UNDERSTANDING THAT HAD ALREADY BEGUN!
...Tehillim/Psalm 104:19 states that the moon is for moadim, BUT the SUN KNOWS when to SET, or ITS SETTINGS as it relates to SETTING the 4 tekufot/SEASONS of the biblical year