I was born in the 1970s and have had a hyphenated name since birth-- both of my parents' last names. Same for my brother.
Don't relate at all to the other poster who felt it was a huge pain and dropped "one of" the names. I don't even think of my last name as two last names at all.
It's a minor pain, sure, but nothing disastrous has come of it in 40+ years. And it's unique, and it's mine, and it's weird and not at all sonorous and it's totally fine. I get checks made out wrong, some credit cards run it all together or cut part of it off, plane tickets can be weird... and it's basically never been an actual hassle. First of all, because those things only happen about 5% of the time, and second because even when they do happen, only 1% of people or machines even flag it, and only 1% of THOSE interactions are not very quickly resolved. I lose about 10 minutes a year of my time to any hyphenated name issues.
(Interestingly, most of those 10 minutes are figuring out quickly that my ~whatever~ has been misfiled under the first letter of the "second" last name instead of the "first" last name. IMO this is because my name is imagined to be My Maiden Name-My Husband's Last Name and it "should" be My Husband's Last Name, so they very very occasionally misfile it that way.)
I feel like those without experience are overstating the issue with computerized forms and such. This used to be a little bit more of a problem in the 80s and 90s but it rarely is flagged as "you can't use special characters" or whatever anymore. Too many people, especially younger than I am, have hyphens in their names. Let alone O'Donnells or what-have-you. It's so, so not that serious IME.
I'm completely outing myself here on DCUM, but I even gave my totally weirdo hyphenated last name to my kid, on her birth certificate, as her second middle name. (She has my husband's last name for a reason having nothing to do with patriarchy or spelling/hyphenation.) She is very proud of her extremely long name.
Not meant in a snarky way, but maybe I just have a lot of pride in my name that overrides any incredibly minor inconvenience? I'm 100% convinced only me, my brother and my daughter (as a middle name) have ever had my last name in the history of the world. And I'm not 100% convinced of almost anything, it's just that much of an oddball name.
In conclusion-- ha! If I saw a kid with a hyphenated last name, I would think nothing of it. Actually, I'd kinda think it was cool, since we would share that experience.

Especially since it was pretty rare when I was growing up. I would think their parents are most likely either left-leaning, British or from a Spanish-colonized culture. And move along with my day.