Our tenants can’t login to the existed project. We have redirect to the https://manage.auth0.com/welcome/ page. When I trying to type my project name the system shows that name is already taken.
Welcome to the Community!
It sounds like you are saying the admin can’t login to the tenant. I can help you with that. 
Would you please DM me the email you are trying to log in with and the name of the tenant/account you are trying to access?
Here is the solution for anyone else who runs into a similar issue:
Log out from manage.auth0.com, and log back in with the email/account that received the email invite before clicking the invite link. Please ensure you do this from the same browser session.