Start over with stating your goal as it has been interpreted ambiguously.

Do you want to change the name of an existing material to a different name?

Or you want to change which materials are assigned to some polygons?

You asked how to rename a material group. There is no such thing as a material group. There are things we call materials, and there are things we call polygon groups, and the grouping tool will let you make polygons belong to different polygon groups, and will let you assign a material to a set of polygons. The grouping tool will also let you create a new material, but not to delete or rename a material.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)