In most US states, strictly speaking, a P.E. license is required to offer engineering services to the public. Most states license all engineers as "engineers" and not in specific disciplines (just like lawyers and doctors, for example - they don't license pediatricians separately from internists). These states allow as part of the whole process, taking a "Principles and Practice" examination specific to Naval Architecture/Marine Engineering. Though these states do not restrict disciplines, engineers are not supposed to practice outside of their expertise (even within a discipline), and there are severe penalties for doing so.
A few states (CA, OR, WA, RI, that I know of) have specific disciplines and in these you have to take the specific exam in that discipline, and the license is distinguished by discipline. As far as I know, only WA and OR have a specific NAME discipline (and have for many decades).
As to calling yourself a naval architect, this could be (and has been) held as one means of offering engineering services to the public, and could be controlled. Calling yourself a yacht designer is not generally controlled, since this is drafting services, not engineering. provided you don't describe the work as engineering otherwise.
It is also unlawful to practice engineering, with numerous exemptions, without a license, regardless of how it is described. However, in general US laws have as their basis "public safety", so in general, practice of yacht design is not controlled, as it only involves private parties, not "innocent" public third parties (that is third parties to the designer/builder/owner contract).
This is fairly complicated area of the law and getting more so. Maine recently passed a law that "working on boats under 200 feet" was exempt, but this may not mean offers are uncontrolled, nor does it define "working" as including "...performing engineering calculations and analyses to validate compliance with legal standards to protect public safety...", which is what "engineering" is under the law. This may also change in view of the Ethan Allen accident. This is precisely the sort of event that licensure is supposed to prevent.
As to Westlawn and YDS, they are not ABET recognized, nor are they equivalent under the law, so neither would count in applying for a P.E., noting that some states do not require a degree for licensure. Thus the term yacht designer would be appropriate unless licensed or otherwise qualified as a real naval architect.
As far as writing a book, anyone can do so, whether it is about engineering or ancient astronauts. It doesn't have to be right, and the individual doesn't have to be qualified in any way.
Go to
www.ncees.org and
www.nspe.org for more information.