Who owns your domain name?
The registrant does: the person or business named as the registered name holder with the registrar. If an agency registered your domain in its own name or account, it controls the domain, whatever you paid. Check today. Look up your registrar, log in, and confirm your business is the registrant, with an email address you control as the contact.
ICANN, which oversees domain names, sets the rules registrars follow. Its registrant FAQ says your registrar "must provide you with the AuthInfo code within five (5) calendar days of your request," and that code is what you need to move the domain. It also lets registrars deny a transfer within 60 days of a new registration, a previous transfer or a change of registrant, so moving a domain out of an agency's name can mean a wait.
ICANN also puts duties on the registrant: provide accurate contact information and "respond to inquiries from your Registrar within fifteen (15) days." If the contact email belongs to an agency, renewal notices and verification emails go to them, not you. Our website cost guide covers what a domain and hosting cost each year.