WD external hard drive back up two different computers

Hi Community. I have a 4 TB WD external Hard drive. I've backed up my own MacBook Air 2022 on this hard drive, however I would like to also separately back up my daughters MacBook Air 2020 on this hard drive. I can't seem to work out how to back up her hard drive (when I plug the hard drive into her computer) as it looks like it will overwrite my own back up. When clicking the + button it doesn't let me add her MacBook Air 2020. Is it possible to have 2 different MacBooks backed up on the same hard drive? Thank you.