Language use changes over time. In Indigenous contexts, language alters to suit the shifting nature of cultural expression as this might fit with Indigenous peoples' preference or as a consequence of changes to outdated and colonial modes of expression. For students studying in the discipline of Indigenous Studies, learning to use appropriate terminology in written and oral expression can be a source of anxiety. In this paper, we consider how providing insight into the political nature of language can help students to be mindful and to understand that systems of naming have a political impact on those being named and those doing the naming. This paper reflects the views and experiences of teaching staff at the Indigenous Studies Unit (ISU) in the Faculty of Arts at the University of Wollongong. It comes from our teaching experience, and from discussions with staff and students over the past few years that have conveyed to us a continuing anxiety about language use. (Contains 7 footnotes.)