As-Asalamu alaykum
Adam alay his salam was asked to name the name of every creation and that was before shaytan became a kafir.
and besides when did names convert to Islam? no really we have to think about this because Bilal isnt an Arabic name neither is Ibraheem or Ismael , in Arabic Grammar they are counted as Ism ghayr munsarif , they cant receive a tanween or be in a genative (majroor) state but becuase they were Muslim and Muslims beleieve all the Prophets were muslim therefore it is considered as a Muslim name. i too belive your a Muslim so therfore i consider it a muslim name .
The Prophet peace be upon him only changed peoples names when they had been given degrading names ... the Prophet peace be upon him did say that the best names are those with hmd as their root mahmood muhammad hamid ahmed and so forth.
i feel for somebody to pick at a innocent name that has no negative meaning is petty, if it was you birth name and you were born on fitra .therefore muslim muslim muslim ...
plus we believe that the sun moon and stars are muslim, why? because they serve their purpose! doesnt your name serve its purpose? againMuslim.....
we could go on ...wasalams