I don't think Star Trek would work like that. Its just not in the story's nature to KILL the entire crew of the Yorktown. Especially considering if the TiHo was in space dock it would have also been effected by the probe also generating problems. Really too, if the entire crew of the Yorktown was killed that would be 600ish dead. Something tells me that Starfleet would want to honor their memories. I don't think renaming their ship and giving it to Kirk would be right. I mean I could see Kirk commanding it but one would assume that it would be the Yorktown still. There is a weird connection between Kirk and the Enterprise, as if they both HAVE to be together. Other people commanded the Enterprise and Kirk was stationed on other ships as well. I just don't see Starfleet renaming a ship just so Kirk could continue commanding a "Enterprise." Hence no matter what it seems odd they did that with the NCC-1701 A.