No, the designated name of a US Coast Guard Documented vessel does not need to be original, although it must comply with a few simple guidelines.
If you wish to legally change the name of your Documented vessel, you may proceed to the webform for Vessel Name/Hailing Port Change via the link below:
https://unitedstatesvessel.us/vessel-name-hailing-port-change/
According to the Code of Federal Regulations CFR Title 46.
§ 67.117 Vessel name designation.
(a) The owner of a vessel must designate a name for the vessel on the Application for Initial Issue, Exchange, or Replacement of Certificate of Documentation; or Redocumentation (form CG-1258) submitted to the Director, National Vessel Documentation Center:
(1) Upon application for initial documentation of the vessel; or
(2) When the owner elects to change the name of the vessel.
(b) The name designated:
(1) Must be composed of letters of the Latin alphabet or Arabic or Roman numerals;
(2) May not be identical, actually or phonetically, to any word or words used to solicit assistance at sea; and
(3) May not contain nor be phonetically identical to obscene, indecent, or profane language, or to racial or ethnic epithets.
(c) The name of a documented vessel may not be changed without the prior approval of the Director, National Vessel Documentation Center.
(d) Until such time as the owner of a vessel elects to change the name of a vessel, the provisions of paragraph (b) of this section do not apply to vessels validly documented before January 1, 1994.[CGD 89-007, CGD 89-007a, 58 FR 60266, Nov. 15, 1993; 58 FR 65131, Dec. 13, 1993, as amended by CGD 95-014, 60 FR 31604, June 15, 1995; USCG-1998-4442, 63 FR 52191, Sept. 30, 1998]