It's been Kullback since birth in 1907 to the best of my knowledge, never once Kullbeck.

As a fully anglicized US citizen born in Brooklyn, New York I don't think there's ever been any vowel confusion over the spelling of the name:

https://en.m.wikipedia.org/wiki/Solomon_Kullback

Admittedly I did check as it's not uncommon for mathematicians to have alternate spellings for their names.

Ditto Leibler, born Chicago, Illinois in 1914, no dropped L

https://en.m.wikipedia.org/wiki/Richard_Leibler