On 'Father Ted' what is Mrs. Doyle's first name?

Joan.

Her first name, Joan, is mentioned casually by Ted in the first series, though later episodes play on the fact that she is invariably referred to by everyone as "Mrs Doyle" by seeing her first name ostentatiously drowned out (by such things as ringing bells and telephones) on the very rare occasions when it is said.

https://en.wikipedia.org/wiki/Father_Ted