updated 05/11/2012 AT 9:00 AM ET
•originally published 05/13/2012 AT 9:35 AM ET
While Willis initially settled on the name Dita Blue for the pup, she later decided it didn’t fit, so she took to Twitter to ask fans for suggestions.
The puppy joins the actress’s four other dogs. Of her expanding brood of pooches, Willis wrote, “We are crazy but I love it.”
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