Randy's full name is Randall, after his father.
All quotes from chapter 70, Origin.
There are five Waterhouse children:
(...) equally divided among her five offspring.
Randy is referred to as the eldest son of the eldest son:
Aunt Nina says, "How about you, Randy? As the eldest son of the eldest son, you must have some feelings about this."
There are three pairs of uncles and aunts mentioned by name:
- Aunt Nina (née Waterhouse) and her husband, uncle Red
- Uncle Tom Waterhouse and his wife, aunt Rachel.
- Uncle Geoff and his wife, aunt Anne.
Nina has two sisters:
"(...) a, well, catfight, that you and your sisters were conducting all day yesterday."
Randy's parents are alive and present, and his father was likely involved in discussing how the legacy of his grandmother was to be equally divided among her five offspring:
"(...) My father knows a researcher in Geneva who has done work on problems isomorphic to this one, and sent him e-mail last night. (...)"
The people who were involved in the discussion are called Randy, Tom, Geoff, and Red.
"Well, that brings me to the breakthrough that Randy and Tom and Geoff and I finally came up with at about two A.M. (...)"
From (1) we know that it's his father who is a Waterhouse child, which makes sense, since Randy's last name is Waterhouse as well. From (2) we know that neither Red, nor Tom, nor Geoff is his father. From (3) we can conclude that aunt Anne was born a Waterhouse too, since there has to be at least one other (unnamed) sister and a (yet unnamed) brother, Randy's father. From (4) and (5) we can surmise that Nina's other sister is probably unmarried and that Randy's father was present during the discussion and must be called Randy as well, so Randy was named after his father.
It seems more likely for Randy's father to be involved in discussing the legacy than Randy himself, especially since we learned in chapter 6, The Spawn of Onan, that Randy's father is an engineer, teaching at a state college. It would be weird to leave Randy's father out of the discussion but have Randy in it.
I must admit there is some evidence to the contrary, as uncle Red says to Nina, in the presence of Randy:
This is what your brothers, and brothers-in-law, and Randy and I were debating so late into the night last night.
Which seems to point to Randy's presence during the discussion.