Yazgulyam

What kind of evidence would be considered sufficient reason to change the primary language name?

I would like to recommend that the primary language name be changed to "Yazghulami", and that "Yazgulyam" be listed as an alternate name. Yazghulami is the spelling used in the majority of scholarly literature on the language.

The transcription "Yazgulyam" is an Anglicization of a Russification of the Tajik name of this language (Russian: Язгулямский язык [Yazgulyamskii yazyk] from Tajik: Язғуломӣ [Yazghulomi]). 

The spelling Yazgulyam is rare in scholarly literature. The most prominent source that uses it is WALS, but I can't seem to find their own source for the spelling of the name. Other than WALS, I have found no occurrences of this spelling in recently published scholarly literature (I just completed an MA thesis on this language, which included an extensive literature review). Occurences of this spelling occur relatively frequently in online sources, and when these include a list of citations, the Ethnologue is often one of them. If the Ethnologue's reason for spelling it "Yazgulyam" is based on sources that cite the Ethnologue, there may be a problem! Furthermore, the Ethnologue should base its spelling choice on peer-reviewed sources, and should choose the most widely-accepted variant of the language name. 

Joy Edelman, the most prominent scholar of this language, has continued to publish papers on Yazghulami since the 1950s. The majority of these are in the Russian language, but in her publications in English she uses the spelling "Yazghulami".

A few academic sources: 

Edelman, D.I. 1980. "History of the consonant systems of the North-Pamir languages." Indo-Iranian Journal 22, 287–310. [spelling used is Yazghulami]

Edelman, D. Joy I., and Leila R. Dodykhudoeva. 2013. "The Pamir Languages." In: Gernot Windfuhr (ed.), The Iranian languages. Routledge, pp. 849-862. [spelling used is Yazghulami]

Grierson, George A. 1920. Ishkashmi, Zebaki, and Yazghulami. London: Royal Asiatic Society.

Jamison, Rachel. 2022. The Enclitic =da and the Marking of Indicative and Subjunctive Mood in Yazghulami. MA thesis, Dallas International University.

Müller, Katja and Tiessen, Gabriela and Abbess, Elisabeth and Tiessen, Calvin. 2005. "Language access and Tajik language proficiency among the Yazghulami of Tajikistan." In John M. Clifton (ed.), Studies in languages of Tajikistan p. 107-149.

Narin, Matilda. 2016. Phonological features of Yazghulami: A field study. MA thesis, Stockholm University.

Payne, John. 1989. "Pamir languages" in: Rüdiger Schmitt (ed.), Compendium Linguarum Iranicarum, 417–444. Wiesbaden: Reichert. [spelling used is Yazghulāmī]

Zarubin, I. I. 1936. "Two Yazghulāmī Texts." Bulletin of the School of Oriental Studies, University of London 8. 875-881.

Non-academic sources:

https://en.wikipedia.org/wiki/Yazghulami_language

https://omniglot.com/writing/yazghulami.htm

A few sources use the similar spelling "Yazgulami" (with a "g" instead of the fricative "gh"):

The Red Book of the Peoples of the Russian Empire https://www.eki.ee/books/redbook/yazgulamis.shtml

Wohlgemuth, Jan and Cysouw, Michael. Rethinking Universals: How Rarities affect Linguistic Theory, Berlin, New York: De Gruyter Mouton, 2010.

Sources that use the spelling "Yazgulyam":

World Atlas of Language Structures (WALS Online) https://wals.info/languoid/lect/wals_code_yaz

OLAC http://www.language-archives.org/language/yah