The former Hannah Montana actress and singer, who has been dating Hemsworth on and off for over two years, confirmed that they decided to name the dog Ziggy.
Posting a picture of their new pet, Cyrus wrote on her Twitter page: "Got Liam THE best bday pressie ever! (sic)"
When a fan then asked if the dog's name was Daisy Dukes as reported, Cyrus wrote: "Liam wanted to name her that! I said NOOO WAY! Shes an angel! she loves her bro & sis too!"
In 2009, Cyrus decided to name another pet dog 'Mate' after hearing Hemsworth use the term. She said: "I just bought a little German Shepherd and I named it 'Mate' because I always say 'mate' now to Liam. So that's my little German Shepherd dog's name."
The star has previously joked that she grew up in a family that had "10,000 dogs".
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Watch the trailer for Miley Cyrus and Liam Hemsworth's movie The Last Song below: