There is a cheap and even for current humanity achievable way to rotate a black hole; change your frame of reference. That is not only true for angular momentum but linear momentum and position. Those are entirely dependent on the observer and their frame of reference. Spin, magnetic charge and mass are not.
Two black holes who differ only by their position, linear and/or angular momentum but are equal in all other parameters are not distinguishable from simply seeing the same black hole twice from a different perspective.
Two black holes who differ in any of the three properties of mass, spin or magnetic charge are distinguishable by those properties (but even that is arguable to some extend).
edit: The rent prices of a planet don't matter since frame of reference is an actual term here, there is no frame of reference more valid than any other for determining the linear or angular velocity or the position of a black hole.
Two black holes who differ only by their position, linear and/or angular momentum but are equal in all other parameters are not distinguishable from simply seeing the same black hole twice from a different perspective.
Two black holes who differ in any of the three properties of mass, spin or magnetic charge are distinguishable by those properties (but even that is arguable to some extend).
edit: The rent prices of a planet don't matter since frame of reference is an actual term here, there is no frame of reference more valid than any other for determining the linear or angular velocity or the position of a black hole.