Anyone who is competent to do electrical work can issue the various electrical certificates (EIC, MWC, EICR) for the work without being registered with anyone.
If it is Part P notifiable work (new CU, bathroom work within zones, new circuit), then you have to be registered with one of the Schemes to be able to notify it, or notify the LABC in advance of the work and pay their fee (unlikely to be economic for small jobs). There is also in theory a 3rd party scheme where you can get a Part P registered person to notify if for you, but it requires them to be involved at every stage.
This is assuming you are in England - the situation is slightly different in Scotland.