Why are human titin and mice titin considered the same protein?
Human and mouse titin are orthologs, and can be confirmed through an NCBI query for TTN. 

Orthologous proteins are not the same, per se. They retain the same function, and basically result from speciation: the common ancestral gene got divided between two species. However, the sequence may potentially differ because obviously the species have diverged. 

Homology between the two can be confirmed computationally, through phylogenetic and alignment analyses, but I believe the naming convention Titin for both mouse and Human stems largely from the function of the protein in either organism.

Naming convention and explanations of homology are nicely outlined in this Bio.SE post.