Yes, it is perfectly reasonable for councillors to know who they are electing. However unless it is your standing orders, it cannot be made a requirement to do so.
The Chairman is elected by a show of hands unless a ballot is requested by any councillor.
Remember, the item must be chaired by either the outgoing chairman or a councillor elected for that sole purpose (have a chat before the meeting to decide on someone to fulfil that temporary role - it prevents mums and errs in the meeting itself), they will chair the election process until a chair is elected. The Clerk MUST NOT Chair any part of the meeting.