Why didn't they write 取了 here? 柳云龙 is being interviewed. The interviewer asked: 

柳（云龙）先生，谁给你取的这个名字？
Mr Liu (Clouddragon or Speakingdragon, not sure??), who chose this name for you?

She used 的. Why not write 了？

柳（云龙）先生，谁给你取了这个名字？

I think I can rearrange thus:

柳（云龙）先生，这个名字是谁给你取的(名字）？ Is that where 的 comes from?

PS: I know a guy called 许成龙， I always ask him when he will finally become a dragon. He's not sure.
谁给你取的这个名字？ conveys where you got the name or who give you that name. 

谁给你取了这个名字？ sounds like who have given you such a name, implying who have done that naming because that name might sound unusual, weird/ridiculous/etc.