My girlfriend (who is also a catechumen in the Orthodox Church) was brought up Hindu, and her name is the name of a Hindu goddess. I think that in this case she would almost have to accept a new name on chrismation, because "all the gods of the gentiles are devils" (Ps. 95:5) and you wouldn't want to go around saying "Hi, my name's Lucifer", would you?
If you think about it, the early pagan converts to Christianity didn't change their names to "Christian" names. We have St Dionysios in Acts; probably a follower of Dionysios before converting. St Aphrodite is another saint, that springs to mind, with the name of a pagan deity. And, if your girlfriend keeps her Hindu name, it will be Christianised and that's totally in keeping with the early saints
In the Vulgate, Christ is referred to as "lucifer" (2Peter 1:19). It doesn't seem that St Jerome intended satan to receive such a title, though the King James translates Isaiah 14:12 as a proper noun for satan and ignores it as a reference to Christ. Lucifer, meaning "light-bringer" hardly seems the appropriate name for satan - but definitely one for a Holy Saint.
Edit: Thought I had better add the pertinent scripture...
12 quomodo cecidisti de caelo lucifer
qui mane oriebaris corruisti in terram qui vulnerabas gentes
12 How art thou fallen from heaven, O Lucifer
, (son of the morning???) how art thou cut down to the ground, which didst weaken the nations!
2 Peter 1:19
et habemus firmiorem propheticum sermonem cui bene facitis adtendentes quasi lucernae lucenti in caliginoso loco donec dies inlucescat et lucifer
oriatur in cordibus vestris
2 Peter 1
19 We have also a more sure word of prophecy; whereunto ye do well that ye take heed, as unto a light that shineth in a dark place, until the day dawn, and the day star
arise in your hearts: