Aston Villa Birmingham would have a ring about it, Whitby reckoned, and he promised to raise the matter with club chairman Randy Lerner.
The idea, it seems, is all part of Whitby's insistence that Birmingham must be "globally relevant".
Football fans across the world know about Aston Villa, but they don't know that the club is based in Birmingham, apparently.
This is not the case with, say, Everton, a club which most people automatically associate with Liverpool.
The same could, of course, be said about West Ham, Arsenal, Chelsea and Tottenham Hotspur.
Football fans across the world just somehow know that these clubs are based in London.
All of this is true, but the Villa conundrum has more to do with Birmingham's low profile and relative anonymity than anything else.
Even if Aston Villa were to become Aston Villa Birmingham, would the average Italian, Brazillian or Argentinian fan have any real idea where Birmingham fits into the scheme of things?
It's not going to happen, of course.
The reaction from Villa management to the council leader's suggestion has been incredulous, while supporters websites and chat forums are full of the most scathing abuse directed at Whitby.
It's being claimed now, by the council, that what Whitby actually meant to say was that Villa should change their marketing strategy in order to promote the club "at the heart of Birmingham".
The fact remains, however, that the council leader is involving himself in matters way beyond his remit and shows little or no understanding of the tribal nature of professional football. To borrow a military metaphor, asking Villa to incorporate Birmingham in its name would be akin to asking the Welsh Guards to join forces with the Scots Guards - it just ain't going to happen without blood on the carpet.
I am reminded of the late Robert Maxwell, who until his dying day could never understand why his plan to amalgamate Reading and Oxford United football clubs into the Thames Valley Royals was vehemently rejected by both Reading and Oxford fans and directors. Maxwell knew how to make money, but he didn't understand football.
Mike Whitby, meanwhile, has diverted his attention from Villa to high finance.
He wants to open a municipal bank.
I shall probably be accused of cynicism, but should councils be getting involved in running banks?
Does anyone think they would be any good at it?