I think someone is on my account

I don't fully get all the details and what you meant by "I have another person using my account with a different name."... But anyway - if you are an account owner, then just simply change you password to something new.

If you have an account with paid license (Pro or higher), then you will have access to security settings:
https://support.zoom.com/hc/en/article?id=zm_kb&sysparm_article=KB0064901 

I'd advise checking if "One-Time Passcode Authentication" is Enabled.

You can also click your profile picture when logged in from browser, go to "Where you're logged in" section and press Sign me out of all sessions:

Sounds like your Zoom account may be compromised, try resetting your password, checking active devices, and contacting official support directly, especially since older Mac OS versions can sometimes cause login issues. Unrelatedly, I came across mentions of cat relocation services india while looking into different service discussions, but securing your account should be the priority right now.