When to change name on Social Security after K-1 and marriage

[PeterMcS 3]

My fiancee entered America on her K-1, got a social security card in her maiden name, and we got married yesterday. She intends to take on my last name. Can we go to the Social Security office and change her name immediately? I'm confused by the advice I've seen here, e.g. some people seeming to say we should wait to change her name on the I-485 and I-765 (then they'd send her a new SS card with the new name on it) and others seem to say we should change it after we're married. If there's no problem with changing her name now, I'd prefer not to wait: I'd like to start putting her married name on credit cards, add her to my bank account, etc. (then use her new name on the immigration forms later). If someone could clear up my confusion, I'd appreciate it.