For my opinion… I would say it is a good idea to put a Maori translation under the existing name (as many institutions currently do) but not to change the full name of the society.
By adding the Maori name we acknowledge and honor the other language of New Zealand (well, the other written one, anyway…) but we don’t run the risk of any (more) confusion over what the society is.
The Uni of Auckland, for example, puts ‘Te Whare Wananga o Tamaki Makaurau’ under their standard logo and it looks good. ‘Te Roopu Tuakoi’ (or whatever is appropriate) would fit snugly under the existing nzLARPS logo, although admittedly would become a bit illegible at small size.