There are no generally accepted alternative names for the Tundra Enets language in Russian. There is an outdated name “the language of the Yenisei Samoyeds”, but it referred both to Tundra Enets and its cognate language, Forest Enets.
Yet the Forest and Tundra Enets never considered themselves to be a single people: they had different self-names and never used them to call the Enets belonging to another ethnic group: for that they used other ethnonyms.
In the same way, the Samoyed peoples neighboring the Enets (Tundra Nenets and Nganasans, whose languages are related to Enets) never regarded the Forest and Tundra Enets as one people and also used different ethnonyms for them. Since in all the above-mentioned Samoyed languages (Tundra Nenets, Nganasan, Tundra Enets, Forest Enets) the name of the language is formed on the basis of an ethnonym, the language of the Tundra Enets in all these languages is a different word than the one for used to designate the language of the Forest Enets.