Rumer Willis is "having trouble" coming up with a name for her new puppy.

Rumer posted a picture of the pup on Instagram and added the caption: "Introducing Delilah Rose Blue-Willis aka DoDo aka Yonce Blue-Willis the newest addition to my clan. #wearestillhavingtroublepickingoutaname (sic)"

The 'Hostage' actress has fallen in love with the animal and has taken to the social networking account to post several photographs of the puppy, and she even took the pet pooch with her to West Hollywood salon Nine Zero One over the weekend.

She wrote: "Delilah just getting in some mommy time at her fave salon @ninezeroone (sic)"

Rumer – the daughter of Bruce Willis, 59, and Demi Moore, 52 – will be hoping her latest canine addition doesn't do a runner as her terrier beagle dog Indy Blue did so in July 2012.

The star was left heartbroken when the canine went AWOL so she put up "missing" posters around her Hollywood Hills neighbourhood in a desperate attempt to find the four-legged friend.

However, Rumer was later in luck as the then-four-month-old hound was finally found alive and well.

As with Delilah, Rumer was also struggling to name Indy as she originally called her Dita Blue before changing her moniker and had to ask for help from her social media followers.