Hi,
As you increase the dielectric constant, the modes number increase too. It means there are more than 1 mode propagating in your resonator. So, you have to increase the number of modes in that simulation, what can be done within port1 properties (Number of modes).
Regarding the mode nomenclature in CST, it is the same from EM theory. You can have TE, TM, TEM and QTEM modes depending on the simulated geometrical structure. You can simulate only the port modes checking the box "Calculate the port modes only", and you will see what kind of modes that port has.
Regards.