Caliph in Arabic is خليفة, and that literally means "the one after". It's not very common but it's still used even in daily life for example for a person inheriting his dad's company or something (not in all Arabic dialects though).

The religious significance isn't in the word itself, but in the meaning when for example a huge prophet like Mohammed appoints and declares a certain guy as a caliph, sending a message to people that means that this guy is the best and the most approved among you all. Having that approval from a prophet is a big deal, but it's nothing too religious or any holy.