I think there may be some connection between your Fall River Regan family and my own Fall River O'Regan family.
Although mine is the family of my grandmother, I don't know it very well. I include a partial tree that I have put together based on an interview of one of my aunts some years ago:
1 Robert O'Regan
.. 2 William J. O'Regan d: in Fall River, MA
...... +Eliza Reynolds b: in London, England d: in Fall River, MA
...... 3 William Francis O'Regan b: 08 May 1888 in Fall River, MA d: September 1982 in Fall River, MA Fact 1: LDS Family History Social Security Death Index
.......... +Jane b: 12 February 1909 d: August 1988 in Fall River, MA
...... 3 Agnes O'Regan b: 29 June 1891 in Fall River, MA d: December 1964 in Fall River, MA Fact 1: SS # 016-22-5664
.......... +John Halpin b: Abt. 1891 d: in Fall River, MA
...... 3 Amelia O'Regan b: 19 January 1901 in Fall River, MA d: February 1976 in Middleborough, MA
.......... +John H. Sullivan d: in Middleborough, MA
.. 2 James O'Regan
.. 2 Michael O'Regan b: in Fall River, MA Fact 1: Civil War veteran; awarded a Purple Heart.
.. 2 Joseph O'Regan Fact 1: Was a bartender in Fall River, MA Fact 2: Served as an alderman for the City of Fall River
...... +Catherine Dwyer
...... 3 Robert O'Regan
.......... +Beatrice Bourrel m: 1902 in St. Anne's Church, Fall River, MA
.. 2 Thomas O'Regan Fact 1: Thomas was a baker. Worked with Liza Reynolds O'Regan.
I do not know for a fact the first name of my great grandfather. I do know that in my family, there is also the tale of someone in the family having been involved in some way with the Lizzie Borden case.
I can be reached at firstname.lastname@example.org