Website designer refusing to give up domain and claiming we will lose all positive reviews we've accumulated if we cancel monthly service?

if someone built your website and they charge monthly, can they refuse to give up the domain if you cancel their services and i want to build my own website (what is the process behind cancellation and re-acquisition of a web address)? and slso they are saying the reviews we received while utilizing their webpage... show more if someone built your website and they charge monthly, can they refuse to give up the domain if you cancel their services and i want to build my own website (what is the process behind cancellation and re-acquisition of a web address)? and slso they are saying the reviews we received while utilizing their webpage will be void and affect our ratings... is that allowed?
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