l’aniyus daati, Rav Chaim feels strongly about this because we’re living in a time of shmad that requires extreme measures, per the gemara. To back this up, I found online that davka the name “shira” was the 2nd most popular baby girl name in Israel in 2012. The other names on the list were either modern Hebrew inventions or biblical names that were never (or rarely) used by Jews throughout history.
Bishlama there is no halachic issur against modern names, but as frum Jews we strive to be “muvdal” from all the negative trappings of modernity, especially its incarnation in eretz hakodesh r”l. Names is a critical aspect of any culture, and by borrowing Israeli names, it shows where our allegiance lies…