title - Same movie but with different names

Setting aside working titles and translated titles, there are other reasons why a movie might be released under an alternative title. In the case of Unleashed vs. Danny the Dog, one of the reasons appears to have been heavy editing/censorship:

Already when the movie has been shown in European cinemas, some magazines wrote that the European version was different in some points from the U.S. version. This apparently affected all countries where the movie hadn't been released with the title "Unleashed", but with the title "Danny the Dog". These countries weren't just European, but also states like Hong Kong. The versions can be kept apart right at the beginning because of different titles (except in the U.S., where both versions are called "Unleashed" but differ as "unrated" and "R-rated").

A better example of a movie which was released under an alternative title for similar reasons is Dario Argento's Phenomena which was released in the US as Creepers. The American version is shorter than the original by 30 minutes.

Title changes are sometimes made because the original title might not be understood in a particular market. A famous example is Harold and Kumar go to White Castle which, in the UK, was released as Harold and Kumar get the munchies as the restaurant chain does not have a presence there.

Some alternative titles are chosen simply for better marketing because the original title did not click with viewers. It could well be that some overpaid executive somewhere thought that Unleashed sounded more like the action movie it is than Danny the dog which could well be mistaken for a family movie about a dog named Danny.

There are also some odd cases such as Jackie Chan's Armour of God and its sequel, Armour of God 2: Operation Condor:

In the United States, Armour of God did not receive a theatrical release. The film's sequel, Armour of God II: Operation Condor (1991), was released under the simplified title Operation Condor. Armour of God was subsequently released direct-to-video by Miramax Films, but the title was somewhat confusingly changed to Operation Condor 2: The Armor of the Gods, despite being the first film.

In other words, the sequel was released first and necessitated a name change in the subsequently released original.

Wikipedia has a time-sink here with a list of works with different titles in the United Kingdom and United States.