דא"ר חנינה שמות חדשים עלו בידם מבבל
R'Hanina said: the names of the Months were brought with them from Babylon
The Gemmorah explains the process of adopting the Babylonian names instead of Biblical ones. The WIKI on Babylonian_calendar states that although every month is associated with a deity, Tammuz specifically bears the name of their god.
WIKI also says that the name of the god was widely known (and even worshipped) by the Israelites:
The cult of Ishtar and Tammuz may have been introduced to the Kingdom of Judah during the reign of King Manasseh and the Old Testament contains numerous allusions to them. Ezekiel 8:14 mentions Tammuz by name: "Then he brought me to the door of the gate of the Lord's house which was toward the north; and, behold, there sat women weeping for Tammuz. ..."
Ezekiel's testimony is the only direct mention of Tammuz in the Hebrew Bible, but the cult of Tammuz may also be alluded to in Isaiah 17:10–11:
What are the potential Halachical problems and does anyone deal with that?
