I know my number and my daughter’s, both of which I picked out as easy-to-memorize. Stores and restaurants here have (often worthless) memberships which are accessed by reciting a phone number.
There’s at least one (now useless) 20th-century number I still know, because I’d mapped the 9 digits to 9 memorable letters.
In 1976 I met a lady who worked as a telephone information operator. This was before they had computers to help with their job, and had to use books themselves. I asked her how they usually gave their answers so quickly. She said they had many of the more used numbers memorized. So I tested her on a local office supplies store, a hardware store, a few things like that whose numbers I happened to remember. She knew almost all of them by heart.
The only numbers I can remember are the house phone in the house I lived in when I was about 10, and my first ever mobile phone number. I can’t even remember my current mobile number.
Don’t know if it still is, but the SSN was a required part of the address when writing to someone at a military installation. I learned his well before I memorised my own.
When I got my first license in the early 80’s, I was asked if I wanted to use my SSN as my license number. I declined as that struck even teenage me as a phenomenally bad idea.
When I started college (University of Wisconsin-Madison) in '83, our student numbers were just our SSNs, with an extra “check digit” appended on the end. I guess it was sometime after the 1980s that people generally started to realize that using an SSN for general identification was a bad idea.