Of your two choices, Phoebe fits better with Iris to me - both are more well -known/popular names. But I much prefer the sound of the unusual Athena - it's beautiful.
What about Gaia? - Has both Greek Goddess and nature links like Iris, similar length and syllables but not too "matchy" in sound.
Or Maia? - one of the Pleiades in Greek Myth, and thanks to the "May" link has a slight nature vibe too (like Iris).
Or Lara? - She was a nymph in Greek Mythology, and the name is as well -known/popular as Iris so fits well together I think.
I woud also second pp suggestions of Xanthe, Selene, and Thalia - all have Greek Mythology links but feel a bit less unusual than Athena to me (so fit better with Iris imo.) Xanthe with it's meaning of "golden" fits especially well with Iris to me. Or you could have Ianthe (purple flower and Greek Myth links) if you wanted something very similar to Iris!