Beverley Nichols mentioned in one of his books that his Hungarian neighbours had a cat called Cica — Hungarian for "cat". Hungarian-born photographer Suzanne Szasz also named her cat Cica.
Used to be the case for the Sun, as well as the Solar System, but terminology has changed, and The Sun is now a proper name for a specific star, and the generic term for a system of planets orbiting a star is now "star system." While other stars can still be referred to poetically as "distant suns," they're usually called by their proper names (e.g. Alpha Centauri, Sirius, HD 206250).
George Foreman owned a dog named Doggo.
Many monotheists express loyalty to a god they call "God". Jehovah's Witnesses are notable for being Christians that avert this.
There is a shopping mall in St. Matthews, Kentucky, originally named The Mall. To distinguish it from other shopping malls in the area, it was sometimes specified as The Mall in St. Matthews. Its official name is now Mall St. Matthews.
There was also a shopping mall called The Mall in Kuala Lumpur, Malaysia. It has since changed it's name to Putra Place when a new management took over though.
A common girl's name is Colleen, the English spelling of Cailin, the Irish for Girl.
Same in Greek: Kore (the derived form Cora is much more common)
Pueblo, Colorado. "Pueblo" means "town" in Spanish.
Equineline.com lists at least three racehorses which are named simply "The Horse" or just "Horse".