I voted for an-nye-EES, but I think for me half the time it comes out as that and half the time as an-nye-EEZ, with more of a Z sound instead of an S at the end, if that makes sense?
The [name_m]French[/name_m] pronunciation is most like [name_m]Ah[/name_m]-na-ees (because it has an accent on the ï that breaks up the vowel sounds), but in English I’ve always heard (and said) it as [name_m]Ah[/name_m]-[name_m]NYE[/name_m]-iss (or Uh-[name_m]NYE[/name_m]-iss, which is not much different with my accent).
I pronounce it ah-na-EES (or ah-nye-EES), which as I understand it is close to the original [name_m]French[/name_m], I think it’s a beautiful name. I don’t think that pronunciation sounds like “anus,” though the spelling is similar. It’s certainly no closer than [name_f]Avis[/name_f], and I NEVER hear that criticism of [name_f]Avis[/name_f].