You can start with last names beginning with "A" (for Anderson), go through the alphabet with names for each letter, ending with "Z" (for Zebulon). That gives you at least 27 different surnames, including your own. Using either your first name or middle name, if you have one, can give you some interesting aliases.
I started doing this to keep track of the aliases I was using. I knew if the last one I used started with a "D" (for Davis), then the next one would begin with the letter "E" (for Elliot). Keep a log of names so you'll know where you are, or at least consult your records of the last shop where you needed to use an alias. And I used aliases across different shops and different companies--not just apartments. Doing that kept me on track, too, since I didn't have to remember whether I had used a "O" alias (for Odessa) on an apartment shop with MS Company 1, or a fitness center shop with MS Company 10. It was simply the last alias shop, so the next alias to come would be one starting with the letter "P" (for Petrovian). Ideally, the alias name would not be too memorable because it was very unusual and/or matched that of a famous person (like Obama or Buttigieg or Blagojevich). If you can't think of a surname starting with a particular letter, try the name of a small town or a tree.
And of course, if they needed to see my drivers license, then I have been recently married or divorced and their request is a reminder to visit DMV with the divorce decree or marriage license to update.
By the time I finished with the "Z" name, it was time to start over again. The log helps here, too, to keep from reusing the same name.