The spelling han-geul is from the Korean spelling in the 2000 South Korean Revised Romanization of Korean. Hangul is from the older McCune-Reischauer (MR) transcription Han’gŭl but written without the diacritics (including clarified syllabization) for the sake of convenience or because a computer was not being used, which was often done. Hangul is a very common English spelling. (A modified MR is used in North Korea.)
Within the English Wiktionary, “han-geul” is preferred because it is in accordance with South Korea's Revised Romanization of Korean and with Wikipedia's conventions for Korean language, and because the hyphen clarifies syllabization and pronunciation of 한글 as /han.gɯl/, as opposed to */haŋ.ɯl/ (* 항을, *hang-eul).
From Korean 한글 (han-geul, “Korean script”) (Archaic Korean 한글 (han-geul, “great script”)).