When purchasing your logo, you gain complete rights to your designs. That said, having these rights does not include having a registered U.S. federal trademark for your logo.
You are not required to obtain a U.S. Federal trademark registration for your logo. In the United States, trademark protection comes from using a trademark in commerce in the ordinary course of business to identify the source of your business's products or services. You do not get trademark protection by registering a trademark with the USPTO, but obtaining a U.S. federal registration with the USPTO does provide additional benefits, such as the presumption of nationwide rights and the ability to use the ® symbol with your trademark.
Disclaimer: Kindly note that we cannot advise or provide legal counsel.