People getting the issues live in different systems and/or have different needs, and it also changes with our world getting more digital. One part that doesn't much depend on locality this days would be international travel and money.
For international travel, small kids having a different name is surprisingly painful and can get you stuck in an office for hours until it's somewhat clear you're not kidnapping them (proving you're a parent not being enough). Depending on how it goes your plane could be gone by that time.
Money is the same, there;s a lot less check if you send to yourself or family than to a random stranger. Having a different name can mean your transfer getting stuck for days of back and forth.
Then again, if you're just staying in your town never dealing with anything outside of it, you might never have to think about your name in your whole life.
But most people moving in don't cut all ties with their home country nor never touch their passport again I think.
The kidnapping thing has nothing to do with names, if you only have one parent every country has their rules and you should check them out ahead of time.
As you point out, being the parent doesn't really matter in that case, it needs to be proven that both parent agree on the kid leaving the country.
I never experienced any of what you say as a child. We travelled internationally a number of times, never had anyone tell us she wasn't my mom or anything.
I am not sure what you mean about the money thing. My mom was on my accounts when I was a kid (with different last names) so she could send me money. As an adult, I can't see how sending money would be an issue. My mom and I transfer money to each other fairly often still ($70k recently, went through fine).
I did not stay in my home town. Not sure how they would be relevant.
Again, most people would assume (if they assumed anything) that my parents were divorced, which is incredibly common. Half my friends had different last names from their siblings and/or parent. Blended families are incredibly common.
I am now a dad of two. They have my last name, while my wife (their mom) has a different name. Again, never a problem at doctors or school or anything. They always make you fill out your full name and relationship. Again, super common to have different last names here im California.
Again, a huge percentage of the population has divorced parents, plus all the kids born out of wedlock. That is like half the population that already don’t have the same last name as at least one of their parents. Everyone who deals with the population is going to encounter this situation every day. They aren’t going to be surprised or confused by a kid with a different name as their parent.
I think part of it was because the hospital I was born at was renamed just before I was born, and then demolished not too long after. I've had it trip things up before remembering to mention the original hospital name. Everyone seems generally familiar with the bullshit now, just a matter of remembering to bring it up because they're expecting it.
Passports have your parents name, this might cause the clerk to do a double check to make sure but unless losing you or your children documents you will never run into this. Or if you are travelling without passports (which is okay between some countries) and using documents (like birth certificates) in different languages