“What do Canadian (and other women who don’t take their husband’s name) women do about their children’s last names?”
In Puerto Rico (and many Latin America countries) everyone has two last names and no one changes last name upon marriage. Kids get a last name from each of their parents, the first one which is called “apellido paterno” (and it’s usually the primary last name).
Maria Rodriguez Smith marries James Jones Perez
Maria and James have two kids, Miguel and Susan. Their full names are Miguel Jones Rodriguez and Susan Jones Rodriguez. Their family name is the Jones Rodriguez family.
Flash forward twenty or thirty years and Miguel and Susan are marrying other people and having kids of their own:
Miguel Jones Rodriguez marries Molly Gonzalez Baker and have a kid named Jamie Jones Gonzalez. Their family name is the Jones Gonzalez family.
Susan Jones Rodriguez marries Samuel Martin Munoz and have a kid named Sydney Martin Jones. Their family name is the Martin Jones family.
It’s really not complicated at all once you’re used to it.
Here in the US, since there’s no tradition attached to how multiple last names are passed down, a couple could easily choose which names they want to pass down based on how the names sound together, or what the initials spell out, or how high/low they want the kid to be in an alphabetical list, or whatever other option they want.
Edit — Wanted to add that I kept my two last names when I got married, and if my husband and I ever have kids we’re most likely going to do the last name thing I described above, KidName HisLast-MyFirstLast. The hyphen is added to prevent confusion here. I added a hyphen between my two last names when I moved to the US to make people stop assuming my first last name was a middle name.
Incidentally, since we got married in PR and there all legal documents need to have two last names, my husband’s name in the marriage certificate shows up as [FirstName] [LastName] [His Mother’s Maiden Name], because they wouldn’t process the paperwork with just FirstName LastName for him. Which was quite odd if I may say so myself, I wasn’t expecting them to require him to have two last names in the paperwork.