Speaking as someone whose mom didn't change their name when marrying my dad, with a sister who didn't change her name when marrying my brother in law, with a wife who also didn't change her name when she married me, I think this problem is overblown. I have yet to encounter any actual issues with this.
Sometimes people will assume we aren't married and/or divorced, and people will often call me by my wife's last name and vice versa, but it has never caused any actual problem. Never had any system that assumes we have the same last name. So many people live in blended families anyway, that very few systems/people make these assumptions any more.