No.

[His answer is immediate, with no hesitation at all. This is something he needs to make very clear to Luke.]

I can't ever have that name again, and you need to understand that. If I'm ever going to really accept you, I need to accept myself, first. I'm Asch, not Luke, and for me there's no going back. I need you to keep that name and make it yours until I can finally give it to you.