Do you mean Ba'al? Ba'al means lord in phonecian and was the title of many gods in Cannanite religion. Ba'al Hadad was the storm god of Mesopotamia and probably the Ba'al referenced in the Bible.

Bathsheba is actually the anglicized version of the name Bat Sheva which translated to "daughter of the oath" or "the seventh daughter" depending on what the latter part of the name is translated as. Since it is in Hebrew it has no relation to the god Ba'al, although many of the names in the Bible (good and bad) do have relations to the indigenous Cannanite religion. Villians such as Jezebel (Glory to Ba'al), Sennacherib (Sin has replaced brothers), or the veery common name Mark which means Dedicated to Mars (Roman god of War and Agriculture).

Later on in Christian history many people with theophoric (names referencing gods) names that were Pagan changed their names upon baptism or assumption into the clergy. An easy example is Mercurius who started the practice of Regnal names in 533 for Popes by assuming the title Pope John II.

So short answer, no, Bathsheba's name had no relation to a pagan god, but even if it had, there was no reason why it would be an issue at the time. The religion of Abraham was somewhat fluid at the time, with Soloman installing pagan gods in his temple and later Ahab and Jezebel worshiping Ba'al. This was not looked upon well in the Bible, but most likely it was later theological griping about the purity of their religion. The book of Deuteronomy was "found" during the religious reforms of King Josiah and allowed him to point to a supposedly ancient tradition that they had abandoned. This strikes me more as a "rally around the flag" approach than actually signaling a return to some lost practice.