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Which in turn may come from the same root.

> From Proto-Italic kelizris, perhaps root cognate with clueo, from Proto-Indo-European ḱlew-; alternatively (if the rare meaning of "swift, in rapid succession" is to be taken as primary) connected with celer (with Greek κέλλω from a root *kel-). Jackson An Etymological Dictionary of the Latin Language (1828:77).

Four citations given: https://en.wiktionary.org/wiki/celeber#References

I was going to make the same point!

Wiktionary notes that celer and celeber could be related but are likely not. (I'm not sure whether there's more recent debate on this point.)

https://en.wiktionary.org/wiki/celeber#Latin

Yeah, a celebrity is someone who is celebrated. The “quick rise to fame” explanation seem like a folk-etymology.