Congrats! Double middle (and first) names are common in my family. Sometimes, you run out of room on forms but otherwise, is not a problem. My mother was Mary-Sue Natalie-Jane and then hyphenated her maiden & last!!
FYI, You do NOT HAVE to fill out the paperwork before you leave. The nurses are a PIA about it but they cant make you if you cant decide. You have until you need a birth certificate. DD2 wasnt named for nearly 10weeks. We finally had to decide so we could get a birth certificate and SS number for taxes. Otherwise, she was baby girl X. You just have to go back to the hospital and record the name and notify drs and the ins when you do choose the name but if you're not ready, then dont let anyone pressure you!!
dd1 10/05
dd2 11/09
and ... a mini poodle!