Is San Jose State a Religous Name for a State-Run Secular Institution?

California-State-Normal-School-San-Jose
A 1910s era postcard showing the State Normal School at San Jose campus and Tower Hall with a colonnade in front.

Is “San Jose State” a religious name for a state-run secular institution?

Our forthcoming book on California State in San Jose and Beyond discusses this issue, and the fact that the school being named after the Catholic Saint Joseph may violate separation of church and state.

What do you think?