If I understand your question correctly, you receive a set of modes in the mode list that have similar field intensity profile(doughnut shape) and TE polarization fraction and you want to distinguish which one is TM01, TE01 etc.
To do this, you need to look at the polarization of the modal fields, which is the main distinguishing feature of the modes in your list as we can see in the following picture:
In this situation, the vector plot of E fields can be a very useful tool. To demonstrate this functionality, I have prepared the following fiber_modes_example.lms (1.9 MB)
that finds four modes in a generic fibre structure. All of them look very much the same when we look at the mode list and intensity profiles:
Nevertheless, if you go to the objects tree and visualize the modal fields in the Lumerical visualizer, you can switch to the vector plot in order to display the E fields polarization and easily distinguish the separate modes: