You will be issued your Employee Number (used to be called Service Numbers until the introduction of JPA) on day 1 when you join the RN.
You will be issued an 8 digit number beginning with 3, so something like 34567890. Don't ask why it begins with a 3 - it just does.
Service numbers used to begin with a letter (C - Male Officers and Male/Female doctors, D - Male Rating, V - Female Officer, W - Female Rating, P - Royal Marines) followed by a check letter, eg D212121X. (Edit - BTW this isn't someone's actual number!)
However, now all new Armed Forces members get issued the new style of number.
Ship rat, Handler is talking about historical numbers which have long since gone.
You get your number as soon as you join. In your case you will get one of the new style JPA numbers which start 3*******. This is a very new system, most people who joined the Navy (before October last year) have a number like
D******x (male ratings)
W******x (female ratings)
C******x for male officers
V******x for female officers
and P******x denotes a Royal Marine I believe.
Hope this helps.
You'll notice that under the new JPA numbering system it is impossible to tell whether someone is male, female, officer or rating, which may prove problematic.