Although really, early first-season Kirk is the exact same character as Pike -- a serious, driven, brooding, lonely starship commander. He only evolved into a different character as Shatner's performance influenced the role and (probably) as the writers came under network pressure to make Kirk a more conventional '60s action hero.
After all, the name change to "Christopher Pike" happened very shortly before shooting began. For most of the development process, the captain was named Robert April (which eventually got used as the name of a separate character in the animated series), and I think it was briefly Winter or something before he settled on Pike. So changing "Pike" to "Kirk" was just another name switch to start with.
So theoretically, Roddenberry could've just hired Shatner to take over the role of Pike, the way pilot actors are often recast in the series (like Willow in Buffy
, Ginger and the Professor in Gilligan's Island
, Father Mulcahy in M*A*S*H
, the entire pilot cast of the UK Being Human
, etc.). And by the same token, he could've just recast Dr. Boyce with Paul Fix and then DeForest Kelley (who was the actor he wanted all along anyway), since Boyce, Piper, and McCoy are also essentially the same character. But instead he decided to change the names each time he recast a role. Maybe that was because he had the foresight that he might want to recycle the pilot as a flashback (especially once the network pretty much nixed the entire pilot cast as inadequate), or maybe it was just because he kept changing his mind about what to call his characters.