A public PGP key (or "certificate") as seen on the key servers or in your PGP application is a bundle of several pieces of data:
- A public RSA key (i.e. modulus and public exponent) (or a public key for another signature scheme) – the main key.
- A bunch of user identities (name, mail address, etc.) for this public key
- maybe one or several sub keys (for the same or other public key encryption or signature schemes)
- maybe digital signatures of the subkeys signed by the main key
- digital signatures of the identities (or combination of main key and identity) signed by the main key
- maybe digital signatures of any combination of main key and identity, signed by other keys/users. These express trust of these users that your key belongs to a specific identity.
The private key corresponding to your main key and maybe private keys corresponding to the subkeys are the ones protected by your passphrase, but as long as these don't change, your passphrase still works.
There also is a key identifier, which is some kind of hash of the main key.
The identities and subkeys are each signed individually, so you can later add more identities or remove all but one using the command lines explained by Jens – I won't repeat this, as tool usage is off topic here..
Key servers will usually only add data to a key (if it is valid), never remove any, so once your key (with identities) is public, it will stay so. This is a case of The internet never forgets.