adding existing email account on new MacBook Air

its hotmail or outlook.

whenever I try to open it, has a grayed out user which isn't mine. can't delete it so therefore I can't even use my password.

Sounds to me like you are not an Administator in the user account you're using? If you go to System Settings-->Users and Groups, is your user account shown as Admin?

I would suggest the following:

1. Remove the email account from Apple Mail: Log out of or remove email accounts in Mail on Mac - Apple Support
2. Add the email account back in: Add email accounts in Mail on Mac - Apple Support

What type account ?

Is it a Gmail or other