I like it.
I know a few
Siri's (pronounced the same way you do) and they're all lovely People.
Iris is adorable too.
I don't think it's too matchy when I say it out loud, but when I read it I do notice the similarity. I personally don't mind.
Some suggestions:
Iris &
Asta /
AstraIris &
CleoIris &
SaraIris &
SelmaIris &
SigneIris & Siren [see-REN]
Iris &
CleonIris &
ErikIris og
Isak (maybe a bit matchy)
Iris &
Nero