Peter Pettigrew pode be named for her father.

Peter Pettigrew, a Death Eater who’s most known for giving Harry’s parents’ location to the Dark Lord and turning into a rat, may have been named for Rowling’s father Peter Rowling.

“You’ve been hiding from Voldemort’s old supporters. I heard things in Azkaban, Peter … they all think you’re dead, or you’d have to answer to them … I’ve heard them screaming all sorts of things in their sleep.”
_{^{- Harry Potter and the Prisoner of Azkaban, Chapter 19 (The Servant of Lord Voldemort)}}

Further evidence that this might be true is that the book after Pettigrew is introduced, and also a book in which he plays a large part in restoring the Dark Lord to a body, is dedicated to her father Peter.

“To Peter Rowling,
in memory of Mr Ridley
and to Susan Sladden,
who helped Harry out of his cupboard”
_{^{- Harry Potter and the Goblet of Fire (dedication)}}

However, as Valorum suggests in the comments, it’s also possible that Peter Pettigrew had instead been named after Rowling’s professor, Peter Wiseman, instead.

It might have been a joke

JK Rowling is a fiercely private individual. She has gone to tribunal and won a case to prevent fotografias of her son from being published without her own permission.

It would not be irrational to assume that any resemblance of a death eater to someone in Rowling's life (as much as we know about it) is nothing beyond a coincidence.

Além disso, o Igreja da Inglaterra mandates that every child have 3 Godparents, two of the same sex and one of the opposite sex. Considering that she has Godparents for all her children, that's upto 9 people (5 women and 4 men) whose names were potentially used as Death Eaters.

A look at this local also shows that all her friends and family have contributed names to the good characters. Example:

Jill Prewett :: Friend Jill Prewett was a flat mate of Jo’s. Jill and Aine Kiely are the subjects of the dedications of Harry Potter and the Prisoner of Azkaban, stating “To Jill Prewett and Aine Kiely, the Godmothers of Swing.” Jo used her name in the Harry Potter series as the maiden name of Molly Weasley (Molly Prewett).

Ernie Rowling :: Paternal Grandfather Ernie Rowling is the paternal grandfather of Jo. He ran a grocery store with his wife Kathleen called Glenwood Stores in Station Road, West Mors. The bus driver of the Knight Bus, Ernie, is named after him.

Ronald Ridley :: Family Friend Ronald Ridley was a family friend. Jo used his name Ronald as the name of Harry’s best friend, Ron Weasley. Harry Potter and the Goblet of Fire was dedicated to him, stating “To Peter Rowling, in memory of Mr. Ridley and to Susan Sladden, who helped Harry out of his cupboard.”

Analysis of context

This is the entire quote:

I have one last hope for you, which is something that I already had at 21. The friends with whom I sat on graduation day have been my friends for life. They are my children’s godparents, the people to whom I’ve been able to turn in times of trouble, friends who have been kind enough not to sue me when I’ve used their names for Death Eaters. At our graduation we were bound by enormous affection, by our shared experience of a time that could never come again, and, of course, by the knowledge that we held certain photographic evidence that would be exceptionally valuable if any of us ran for Prime Minister.

Looking at the entire thing it becomes apparent that it was not a one off comment but part of an extended discussion on sticking with friends you graduate with.