From Hamelin to Huitzuco

I am searching for my origins.

The Piper note I just wrote did not lead far. Now I am following another lead. Huitzuco 1874, a hundred years or so before and another mispelled (?) name Urriza. A Esteban Urriza was a mine owner in San Luis Potosí. In Huitzuco, my mother's hometown, far from San Luis Potosí, a company Urriza, Thébénet, y Arnaiz; operating  a mercury mine was there in 1874.

My uncle Andrés Figueroa Uriza, claims that a Taxco miner by the name of José Uriza adopted our ancestor Ignacio from a wealthy lady that did not want to own him early in her life, and gave him his name. When she changed her mind and wanted her child back, the miner sent him to Huitzuco, where he had friends (relatives?) to hide the boy from her. All the Urizas from Huitzuco come from that boy.

The company owning the mine eventually folded, and President Porfirio Díaz's father in law, Romero de Terreros took the mine before the 1911 revolution started in Huitzuco, on February 28.

Is Urriza the same as Uriza?