Here's what we did.
Let's say I married a man with the surname Smith. Our two sons in real life got four names.
One was (and this is not the actual names) Robert Steven Oglethorpe Smith, the other was Matthew Edward Oglethorpe Smith. In other words, two normal names, then my surname as a second middle name, and his surname as their legal surname. Not hyphenated. Just two middle names. Over the years both of them have pretty much stopped using "Oglethorpe", because filling out paperwork with the four names is a bit tedious. I wish they'd use it all the time, but not a biggie.
And I constantly remind people that so many people marry, have a kid or so, divorce, then remarry. And then someone invariably has a different last name, and everyone is just fine with that, no matter what the woman chooses to do about her last name.