I've seen Brandon James (KillMe) credited in multiple places.[1][2] James left iD mid-development of Quake 3, so the rest of the level design team likely also contributed after that point.[3]

1: https://www.quora.com/Quake-series-Who-was-the-level-designe...

2: https://www.shacknews.com/article/101156/rocket-jump-quake-a...

3: https://www.shacknews.com/article/181/more-on-bjames-id-depa...

First appeared in Quake 3 Arena’s public demo