It absolutely has been a non issue for me.
schools, gp’s etc manage fine addressing letters to “dr x and Mr y”.
my dc were asked once who I was when I was travelling alone, but that was before they’d asked for passports so nothing to do with names. We travel several times a year with the dc’s sports and in 18 years never had an issue.
even when I had to take step dc to a&e for a broken bone it was automatically assumed I was mum, I had to point out I didn’t have PR and couldn’t consent, and they needed to ask dh.
dh on the other hand, has had a nightmare after splitting with his ex. If she didn’t put him down on school, gp forms as their dad we actually had to get solicitors letters to force them to speak to him without her present. And that was with the same name. He was genuinely worried that if the dc had my name and we split (his ex had an affair) it would be an absolute nightmare.
like I said, me in a hotel room with my 15 year old doesn’t raise an eyebrow. A 50 year old man in a hotel room with a 15 year old with a different surname is often a phone call to the police.