All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallAllaahu ‘alayhi wa sallam, is His Slave and Messenger.
However, it should be noted that bearing a name meaning 'God is with us' or 'God is with me' is not recommended because such a name implies self-praise.
On the other hand, listening to music is an entirely different issue; it is impermissible to listen to music regardless of the person who is playing it. Music is prohibited in itself as evidenced by the texts of the Quran, Sunnah, and the sayings of the early Muslim generations from among the Companions and righteous predecessors. For further information, please refer to Fatwas 81239 and 81545.
Allaah Knows best.