I told my parents a few months ago that when I change my name (won't happen for a while yet), I will take another last name because I'm simply too easy to google from my last name. I don't want people to "find" my history that easily.
They for sure didn't like it, but I spent some time explaining to them that it's not because I want to distance myself from them in any way, it's for safety. A few days later, they were seemingly fine with it. It does however help that our last name is a longer and rare variant of one of the most common last names in my country, so I'm simply changing to the "generic" version, which will make my old self impossible to find since guessing the extension to the last name will be close to impossible - there are hundreds of them. So I'm kind of keeping the root of my family name, but dropping the specifics. They found that easier to accept than just taking a random name.
Obviously that's not an alternative if you're taking your wife's last name, but I think getting through to them that it's not because you're distancing yourself from your family is the most important.