Hungarian Historical Phonology hagyma
hagyma 'onion'
First attestation/Old Hungarian data
Place name Hagymas, 1211 (EWUng)
Important dialectal forms
hajma (ÚMTSz: 787-788, s.v. hagyma)
Uralic/Ugric/Pre-Hungarian reconstruction
Disputed:
Zhivlov 2014: *kaćmi 'onion'
UEW: PUg *koćmɜ (*kaćmɜ) 'a species of bulbous plant; zwiebelartige Pflanze'
Loan etymology
← Turkic, cf. Chuvash kǝ̑šmi 'Rutabaga' (Gombocz 1908)
Cognates suggested in earlier research
UEW:
Mansi: West (P) kośəm, (LO) χōśman 'eine zwiebelartige wildwachsende Pflanze, deren Stengel und Wurzel als Suppenwürze gebraucht werden; Zwiebel'
Komi: komiʒ́, kúmić ’spring onion’
Udmurt: kumi̮ź ’garlic’
Commentary
The Uralic (Finno-Ugric) etymology of Hungarian hagyma 'onion' has been widely accepted and it is even mentioned by Zhivlov (2014: 130) who reconstructs *kaćmi (= *kaćmə). However, the Uralic cognates manifest irregularity that makes the etymology problematic. This was noted already by Gombocz (1908) and has been recently discussed by Holopainen (2022: 106). Hungarian hagyma would be the only example of gy < *ćm, and it is dubious whether such a cluster can be reconstructed based on the Permic forms. A cultural word like 'onion' can well be a loanword, especially as the spread of the word is limited to three branches of Uralic that have been historically adjacent to each other.
Gombocz noted the possible connection to Chuvash kǝ̑šmi 'Rutabaga', considering it possible that the Uralic words are borrowings from Turkic. Gombocz acknowledged problem in this explanation that the Chuvash word has no cognates in other Turkic languages. Rédei & Róna-Tas (1980: 126–127) have assumed that the Chuvash word is a loan from some form of Uralic but as noted by Holopainen (2022), this is not clear as long as the background of the Uralic words remains uncertain. It is also possible that the Hungarian, Permic, Mansi and Chuvash words are loans from some unknown source.
(Note that Holopainen 2022 mistakenly mentions that Chuvash kǝ̑šmi means 'onion'.)
Conclusion
The Uralic words are likely parallel loanwords as the reconstruction of a Proto-Uralic word is impossible; connection with Chuvash require further research.
References
EWUng: 509, s.v. hagyma: PFU
Gombocz 1908: Hu, Permic, Ms ? ← Turkic
Holopainen 2022: 106: not PU, loans from unknown source
MSzFE: 241-242, s.v. hagyma: PFU
UEW: 164-165, s.v. koćmɜ (kaćmɜ): PFU Uralonet
Zhivlov 2014: 130: PU