Is it Tāłtān or Tahltan?

Good question!

The members of Dah Dẕāhge Nodes̱idē, (the Tahltan Language and Culture Council) and many of those working on the language use the term Tāłtān to refer to the language specifically, and Tahltan for the people or Nation or Territory.

The language is also referred to as dah dẕāhge ’our language’ or didene keh ’this people’s way’.

So if you want someone to speak Tāłtān you could say:  didene keh hodindē!