Speakers of this language generally consider the name Yuan to be pejorative. They generally call themselves Khon Mung (or Lannathai, or Northern Thai--or Western Lao, across the border). The language is generally known by one of these terms, or as Phayap. The term Yuan is still used for the distinctive (and now all-but-dead) Lannathai script.
Most linguists consider Northern Tai to be more closely related to Thai and the other Chiang Tai languages than Lao and the other Phu Tai languages, but the distinction is never easy to make, as the language families form a continuum with few sharp dividing lines.
See also: Thai Yuan