Never let an agency own your accounts
Your domain, hosting, Google Business Profile, analytics, ad accounts and phone number should all be in your name, with the agency holding access you can revoke yourself.
Why does it matter whose name the accounts are in?
Because ownership decides what happens when the relationship ends. If the accounts are yours and you revoke access, work stops and you keep everything. If they are the agency's, leaving can mean losing your domain, your reviews, your ad history and your phone number.
This is rarely malicious. It usually starts as convenience during setup and nobody revisits it. The problem only appears at the exact moment you have least leverage.
What should be in my name specifically?
The domain registration, the hosting account, the Google Business Profile, Google Analytics and Search Console, any ad accounts, the CRM, the phone number, and any AI model provider accounts being billed for your usage.
The test is simple: for each one, could you log in today and remove your agency's access without asking them? If not, it is not yours.
How do I fix it without a fight?
Ask for ownership transfer in writing, one account at a time, while the relationship is still good. Most agencies will do it without argument, and the ones that resist have told you something important.