If an electricity supplier does not routinely use application forms, consider whether you should request a supply in writing. One person can give notice if that person wants to take responsibility. If you are a joint occupier who wants to share liability, ensure that everyone living in the property signs the application form, letter or contract.
If one joint occupier moves out and you move in to take her/his place, there is nothing to prevent you from giving notice specifying that you are replacing a joint occupier or arranging a new contract. Liability depends on who signs the new arrangement.