Asking math PhD admissions for a decision sooner, given that I have received an offer from a good school Can I ask other math PhD programs that I've applied to whether they could give me a decision sooner than later, as I've gotten an offer from a good program?  If so, should I name this program for them in my email or keep it private?
You can ask, but the most likely answer is that no information can be given. Decisions may not be finalized until near the deadline. There may be regulations that prohibit giving out information to individuals prior to agreed-on dates. 

Mentioning the other problem does you no good and might possibly do harm. The admissions committee isn't going to disrupt its procedures because of such information. 

I'd suggest that you just make a decision. 

Another possibility, of course, is to ask the program that accepted you to let you delay your acceptance for a bit - a short period. They may be willing or not, but if you are a really good candidate the chances for success here are a bit better than for the other option. (My opinion, only)