Both Final Fantasy VII Ultimania Omega and the Final Fantasy X-2 Ultimania, suggest that Shinra of Final Fantasy X-2 has a connection to the company of the same name in Final Fantasy VII.
From Final Fantasy VII Ultimania Omega:[1]
Shinra is a boy who supports the Gullwings, the group which the main protagonist, Yuna, belongs to. He carries a name that gives him an association to the Shin-Ra Company, and he is researching a method that could utilize the energy of "the life force that flows through our planet." The results of this cannot be seen in FFX-2, but maybe one day his descendants will establish a "company that supplies the energy of the planet"?
In the Final Fantasy X-2 Ultimania Kazushige Nojima said the following:[1]
After quitting the Gullwings, Shinra received enormous financial support from Rin, and began trying to use Vegnagun to siphon Mako Energy from the Farplane. But, he is unable to complete the system for utilizing this energy in his generation, and in the future, when traveling to distant planets becomes possible, the Shin-Ra Company is founded on another world, or something like that....... That would happen about 1000 years after this story, I think.