I didn't get married until my later 30s, and ultimately didn't change my name either with AEA or legally. Have only had a few times it mattered...and I can tell when "close personal friends" (spammers, and occasionally utility companies) contact me calling me Mrs. His Name. I actually did debate it, and my husband was one of the first to say it sounded like a big pain to change it. Meanwhile, I know many people who professionally go by their ex's name because that was how they were known in the business.
You do have to make sure your name is listed along with your spouse's on utility contracts (if legally you DON'T change yours)...and that ultimately your paycheck goes to the right legal name if you do have a difference. It gets trickier for me when people use their married name for publicity, introductions, etc, and then their maiden name is still connected to their email address. But it's a personal decision, and I can see both sides of whether to change your Equity name. Just hope for the chance to be able to proof your bio/program info. (Yes, it's in the Equity contract, but still one I have to fight to remind companies of...didn't happen on my last one for instance. Luckily the typo was just an errant set of italics in mine.)
Editing to add more thoughts: As another thought, maybe you can have parentheses around your "other" last name in your email signature? Including however you list yourself in a given program like Gmail? If you do use the email for both work and personal, especially.
I do think it would be kind of nice to have different names for different "worlds" - there are some folks who call me by my initials versus first and/or middle name, and I don't "mind" being called Mrs. His Name most of the time. I certainly introduce myself as His Full Name's wife when I meet someone who may not get the connection, but I know we have one. Certainly Mr and Mrs. His Name is easier to write on invitations. I do love when spam/bulk mail goes to The My Name Family, or he's occasionally called by my last name.
I think the big thing to do is make a decision and stick to it. I had one singer friend who - after being married for a while - kept changing whether she then wanted to be listed professionally (non-union) with or without her husband's name. I still don't remember which is the "right" one now. Certainly anyone has the right at any time to change their name, but right at marriage to me is the most understandable time to do it if you're going to. And as I mentioned earlier, I have several friends who are "stuck" using their ex's last names as that's how everyone knows them professionally - they tried to change back and it was too confusing they found. I think our business is much more understanding of having a difference in names than some other areas, too, simply for the whole stage name factor, regardless of whether someone is married.
Erin