The Dark Knight star and her actor husband Peter Sarsgaard welcomed their second girl in April (12) and Gyllenhaal admits they had the tot's name picked out long before she even fell pregnant.
She tells U.S. talk show host Jimmy Fallon, ""We thought of her name when we were at this concert that Patti Smith played at and she played Gloria and it was a couple of years ago and we thought, 'We'll name our daughter that one day'.""
But the actress isn't a fan of all covers of the track, which was originally recorded by Van Morrison's band Them.
She says, ""My husband played me The Doors' version of Gloria two days after my daughter was born and it was so dirty, I couldn't handle it. It was a super, super dirty version!
""Van Morison has an awesome version, which is the one Patti Smith is covering, but she does hers totally her own (way).""
Gyllenhaal and Sarsgaard, who wed in 2009, are also parents to daughter Ramona, five.