I know plenty of women named Sivan and Aviv. They aren’t dati, but these are common names on Israel. If you are in doubt, speak with a Rav. Especially if your spouse likes the name.
There are gedolim who are into biblical names, and those who are more open to new names. Plenty of common Jewish and especially yiddish names were once new. And lots of people, particulalry the EY crowd are bringing back old names from Tanach that we have lost.
Most importantly, mazal tov and enjoy the baby!