This is purely speculation, but I think Aziz didn’t choose a Muslim or ‘Muslim-sounding’ name deliberately, because he didn’t want reaction to the show to focus on the fact that the protagonist is a Muslim. I appreciate there is a lot of ignorance in the US — and you’re probably right that many Americans would not know what organized religion a name like ‘Aziz’ or ‘Dev’ might typically be associated with — but I also think that the majority of the target audience of this show would know that ‘Aziz’ is a Muslim name and ‘Dev’ is a Hindu one. And given the growing Islamaphobia in the US and the increased scrutiny of Islam as a religion, if the character had a Muslim name, it’s likely a lot of the commentary around the show would’ve focused on this.
Of course, this could have had many positives — as you describe and I agree with — but my guess is Ansari did not want focus to be on that, and felt that choosing a Hindu name would lead to the religion of the character not being a topic of discussion.
As an aside — one thing the show didn’t hide was the geographic origin of the character — specifically Tirunelveli in Tamil Nadu. There is no chance at all that anyone from that state would have the name Dev Shah (except in the extremely unlikely event that this character hails from a Gujarati family that migrated to and settled in Tirunelveli several decades back :)). A name like Ramesh (if he wanted to go for a Hindu one) would’ve been much more appropriate.