The name Busy is a girl's name of Hebrew, English origin meaning "pledged to God". Busy and discussed in our forums with posts like "Rate the Previous Signature!".
From the experts:
Yes, it's a word name, but Busy is also a rare pet form of Elizabeth. And yes, actress Busy Philipps was christened Elizabeth--she was given the nickname because she was such an active child. She must have been happy with the name, because she also gave her daughters adorable unique baby names, Birdie and Cricket.