No. Documented boat names do not need to be original. In this context, “original” can mean “names used by other vessels.”
That said, there are rules to naming your vessel.
Specifically, 46 CFR 67.17 states that “the name designated: must be composed of letters of the Latin alphabet or Arabic or Roman numerals; may not be identical, actually or phonetically, to any word or words used to solicit assistance at sea; and may not contain nor be phonetically identical to obscene, indecent, or profane language, or to racial or ethnic epithets.”
When choosing a name for your vessel, use common sense. The name of your vessel will be associated with you. Choose something that you will be glad to be associated with.
In the event that you wish to change your vessel’s name, you can use this link to update your boat documentation. You can also use that link to update the hailing port.