Should I delete my Phantom to use the name for my Luminous?

From the wording of the OP, the Phantom in question isn't even up to lv70 yet. Most players I know would consider that small fry -- embryonic, even. Since Phantoms will be createable in the future, the most important question is whether OP would need that link skill before the next Phantom creation period opens.

//edit: Another important factor that I'm not seeing in this discussion is the possibility that OP might end up disliking Luminous playstyle just as much as Phantom.

Seems like the OP would at least dislike Luminous' gameplay less than Phantom though. I don't know how much does 10% critical do for a Luminous so the only important question is if the OP can wait about three to four months for that same link skill to which I say it shouldn't be a problem.