For so long I always thought that was his actual name and not a title given by the church. And I wondered why some of the other characters called him "The Vicar". It's just unusal to hear people address him that way instead of his real name, or his name followed after Vicar.
We know that his first name is Michael, since his wife has called him that. But we don't know their last name or her first name. I like to think that her name is Marion though, just like the actress's, just because she sure looks like a Marion to me.
In Vicar of Dibley, most of the characters call the main character "Vicar" or "The Vicar" - even her best friend (who, granted, is a dim bulb and wanted to name her first child "Vicar" after her).
In the U.S., we often call protestant preachers "Reverend" as a sign of respect.
Calling a vicar 'vicar' is a bit of a TV-land cliche. In real life it's rarely used as a term of address like that these days. If you know your vicar well you call him (or her) by his first name, if you don't you call him 'Mr Smith' or 'Reverend Smith'. If you are of the Anglo-Catholic (High Church) denomination you might call him 'Father.'