Brain-Teaser 513

From The Sunday Times, 11th April 1971 [link]

Damon Rigby is my grandfather, and his four children (including Henry) are all married. Aunt Fanny is the youngest and at her wedding to Charlie Jones last week I met four of my cousins; only two of our number have the same surnames and only one is married.

My mother’s name is Mary Rigby and I am her only child. My first name is that of the husband of my oldest aunt, but it is a tradition in our family that blood relations do not carry the same first name.

Aunt Fanny has a niece whose surname is Finch. Amanda has the same surname as Agatha’s sister. Aunt Doris has but a single daughter. Jack Prior has an aunt married to Tom whose niece is Amy Brown. The first name of Margaret’s father is the same as my father’s.

What are the full names of the five cousins?