Many people do this mistake letting somebody else own and manage their domains. They dont realize how important it is, until they got hit with a trouble.
First thing is check whose name is the domain on. Use site like whois.sc etc
Then ask the designer if he can transfer the domain to your account. This process might be require some technical knowledge, u might need some tech help on this, but nothing complicated.
If the designer doesnt want to transfer you should check out the contracts see if there is anything that says about the ownership of your business website and related. If you have the right on those, you could consult a lawyer for this.
But I am pretty sure he would transfer it, its very common practice developer maintain the domain.