If a cheque is made payable to Joe Bloggs plumber or Joe Bloggs, plumber (with a comma), this could be considered as indicating an occupation, and there is no obligation on the bank to check his occupation. In fact, if Joe Bloggs is a plumber, there is no obligation on him to have a bank account for his trade receipts.
If Joe has a business account and a personal one, and this cheque is lodged to the wrong account (for whatever reason), then only Joe can rectify the situation.
If however, he trades as "Joe Bloggs The Plumber" as a trading name, then he should register it as a business name and make appropriate arrangements for those cheques to be lodged to an appropriate business account.