You'd have to get rid of not only Ataturk, but the whole Young Turk movement, and thus 'Turkey'.
A 'caliph' is a claim to rule, or at least be hegemon over, all of Islam.
A specifically ethnic Turkish state would, at best, make a mockery of such a claim.
A rump 'empire' that held claim to the former territory, even if it was a Republic and overwhelmingly ethnically Turkish, could. But such a state wouldn't be CALLED Turkey.