Borrowers 'borrow' the things they need from us ordinary-sized people. Sometimes they need names. Perhaps they misheard
Harriet, or perhaps they heard someone with a Cockney accent (dropping the H) and a taste for making nicknames with a -y; either way, Arrietty is their best take on
Harriet, and I see no point in ditching a beautiful classic in favour of a weakish joke at the expense of a fictional character.