Actually Void what you just said could tie in well with the fact that Jean doesn't have a code name either (the only on really). Mags could symbolically given her a new name to celebrate her ascent to Godhood and it might just stick. I she may not say the line as majestically as the comic and '90s cartoon put it but she just scream, "I am Phoenix", before going postal on someone's ass.
Fire Made Flesh