Model Standing Order 3S:
Unless standing orders provide otherwise, voting on a question shall be by a show of hands. At the request of a councillor, the voting on any question shall be recorded so as to show whether each councillor present and voting gave his/her/their vote for or against that question. Such a request shall be made before moving on to the next item of business on the agenda.
The question is not entirely clear in regard to what you mean by "recorded and named" votes.
The outcome of all votes are recorded - that is what the minutes are for - a record of votes.
When a named vote is properly requested (according to relevant SOs) then the names are recorded.
This doesn't apply one way or the other in relation solely to the annual budget / precept - it applies to ALL votes all of the time.