As written in the introduction on the History Page the first Ship Badge's were often the Captain's Personal Badge possibly similar to Admiral Sir Adam Duncan's RN (1731 - 1804) which he may have had hung on his cabin door as a mark of identification and possession. This badge would have been the only badge allowed and if the Captain intended it would be called the Ships Badge but more than likely the crew gave it that honour.

Its not until the 20th Century that badges made by sailors became an unofficial fashion.

Above is Ruby's Replica  HMS Excellent Badge. 
 
The Badge bare's the 1844 Coinage dipiction of  Britannia 'Boudicea Warrior Goddess of Britain' (defaced).
2 HM Ships have borne the name 'Excellent' which has the motto 'If you want peace prepare for War'.
Badges such as 'Excellent' were first image's on ship's paper much like an address leading to the fashion of ornating ship's with a badge.  

The current HMS Excellent is named after the 1787 HMS Excellent which ended her day's in Portsmouth Harbour in 1830 as Gunnery Training Ship. Gunnery Training moved ashore in 1890 to Whale Island in Portsmouth with the completion of the current HMS Excellent which is the British Navy's oldest Training Establishment still in existance it was also used for Parade Training and the Home of Portsmouth Command Field Gun Crew all of which have ceased at HMS Excellent.
HMS Excellent continued to exist as a Regulating School until it closed as a Training Establishment in 1985 and was agumented with HMS Nelson.

HMS Excellent recommissioned as a Training Establishment in 1994 continuing it's work to train Her Majesty's Sailor's for service afloat and ashore.