Domain
The name of your site, what people type to get there: about $12 a year, and it has to be in your name.
A domain is rented by the year, not bought forever. Stop paying and you lose it, and within months anyone can take it, including the competitor down the street.
Forget the price, about $12 a year anywhere. What matters is whose account it is registered in. If the agency that built your site bought it, the domain is theirs, and the day you leave you do not take it with you.
For a local business a short name with the business name in it beats any invention with hyphens and keywords stuffed inside. Nobody types cheap-plumber-miami-24h.com.
What to do about it
Log into your registrar and confirm you are the listed owner. If you do not even know where it is registered, that is the first call to make.
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