Reese is such a cute name (a la Reese Witherspoon). And there are a ton of great "R" names out there—here are a few of my picks for your daughter-to-be:
Rue has recently hit the spotlight, thanks to the character in the popular Hunger Games series. It's an herb that is regularly used in medicines, and I think it'd be a sweet name that sounds beautiful with Reese.
I love the name Ramona—it's the troublesome little sister from the classic Beezus and Ramona books, and means wise protector. It hasn't been in the top 1000 since the 1980s, but Green Day rocker Tre Cool and actors Peter Saarsgard and Maggie Gyllenhaal picked it for their daughters, which may help it make a comeback.
Rowena is a Welsh name that means famous friend—it's currently well known as the name of one of the founders of Hogwarts, Rowena Ravenclaw, from the Harry Potter series.
Rory is a unisex name that means "red king." It's currently more popular for boys, where it's in the top 500, but it's a sweet name for girls, too. It was the name of Rory Gilmore on the Gilmore Girls.