I'm in much the same situation as you, with my partner being Muslim and I myself agnostic. Even if we are not yet even planning for a baby, names for future children is one of our core disagreements. It is a strange thing. I am fine with our future children being raised as Muslims, since I myself feel as something is missing in my life because of my inability to believe. To have that secure knowledge, that guideline in life, that anchor point I think is a good thing. I am not fine with giving them Muslim names...because I feel that would be denying part of their identity, me, entirely. That is the true reason, though of course, the whole discrimination issue is also very real.
I think one thing you have to ask yourself is why it is so important to you that non-muslims recognise your children's names as muslim? Is it not more important that the name is a good one? Here in Sweden, names like Hussein, Hamid etc. have very negative connotations which means that children with these names have a harder time later in life, when applying for studies and jobs. That is something to really consider, how the name will impact not only their identity as muslims, but also their identity as Americans. Just something to ponder.
Also, when you say "muslim" name consider that one of the most important parts of a name according to Islam is that the name has a good meaning. What origin the name has is of no real importance as long as the meaning is good. Nor if it sounds "muslim" (which I suppose is to say arabic, which really is not the same thing).
As for name suggestions (since that is what you really ask) I would suggest finding names in middle-eastern literature that you both like or in history accounts, such as names from Akbar's courts. Some suggestions:
- Mariam (after Akbar's third wife).