For example, Donald Trump's wife changed her name from Melania Knauss to Melania Trump when she was married, adopting her husband's surname. In this case, Melania can be referred to as "Mrs. Trump" and the couple collectively as "Mr. and Mrs. Trump". However, Mark Zuckerberg's wife Priscilla Chan keeps her surname at birth, "Chan". In this case, the two spouses use different surnames. My question is, for example, can Priscilla be referred to as "Mrs. Chan" or "Mrs. Zuckerberg", or should she only be referred to as "Ms. Chan"? Also, can the couple be referred to collectively as "Mr. and Mrs. Zuckerberg" or must the two spouses be addressed separately?
The only rule is that:
People should be addressed how they want to be addressed.
Interpreting this rule on a case-by-case basis is the challenge.
I don't know how Priscilla Chan wants to be addressed -- Dr. Chan (she is an MD); Priscilla Chan, MD; Ms. Chan; Mrs. Chan; Dr. Chan and Mr. Zuckerberg; even, perhaps sometimes (although I don't see why) Mr. and Mrs. Mark Zuckerberg. Note that their foundation (worth billions) is the Chan Zuckerberg Initiative; this gives us a hint.
What is definite is that, in the case of Priscilla Chan, if you are going to invite her to an event, you need to call her Personal Assistant's Personal Assistant and find out how she wants the invitation to be addressed!
In more normal circumstances, you have to use your judgment based on what you know about the people. There will be traditional couples for which Mr. and Mrs. John Doe will probably be best. If you are addressing an invitation to a couple and the woman uses her own name professionally, it is usually safe to address the invitation to Ms. Jane Smith and Mr. John Jones (or in the reverse order.) However, if the man is notoriously touchy about male prerogatives and can affect your career, you might prefer to play it safer and address your invitation to Mr. and Mrs. John Jones. Or not. The woman may be completely and permanently turned off by being addressed as a chattel (as she sees it).
This question isn't about English, or even etiquette. It is about how to navigate tricky social waters in a time of great change and hypersensitivities.
Oh, and for the President and First Lady, be traditional. The Protocol School of Washington advises:
Envelope, official: Mrs. Trump The White House 1600 Pennsylvania Avenue, N.W. Washington, DC 20500
Letter salutation: Dear Mrs. Trump:
Complimentary close: Sincerely,
Introduction to a group: Melania Trump, First Lady of the United States of America
Introduction, one person to another: Mrs. Trump
Conversation: Mrs. Trump
Brits are easier. they have a Bible for this, called Debretts.
You will make mistakes, but fewer than if you try to shoehorn all your guests into a 20th century pattern where women were wives of, daughters of, mothers of, aunts of, grandmothers of, but hardly ever simply themselves.