I was going to try and submit a record attempt in the next week or so for a 2-player game with my son (who is 6). Does he need a username in order for the record to be posted, or can we just post it under mine?

I've been in 4P records where some players were non-members, you should be fine - and you can change it later fairly easily if they do join later.

When you submit a multi-player run, you need to state which player you are (for example player 1), and your username will fill automatically. The name of the other player is a free text box and you can write whatever you want.

If you write the username of an exist user, then the run will also be linked to their profile. If you write a name which doesn't exist in the site, it will be grayed out (I think that is considered as a "guest").

For example, check out @Sterling runs for LEGO star wars - He had one run with "Brother 1", and a second run with "Brother 2".