Marriage in US: registering, updating passport & visa

[abxxxxxx]

My wife and I are both students in US on F1 visas. However, she hasn't yet updated her name in her passport. Is it possible to get this done in US? Can we register our marriage in US?
Also, how does her F1 VISA get transfered/reissued in her new passport (since I think change of name due to marriage requires applying for a new passport)?

Thanks for helping!
AB