Inn
Old English (in the sense ‘dwelling place, lodging’): of Germanic origin; related to in. In Middle English the word was used to translate Latin hospitium (see hospice), denoting a house of residence for students: this sense is preserved in the names of some buildings formerly used for this purpose, notably Gray's Inn and Lincoln's Inn, two of the Inns of Court (see Inn of Court). The current sense dates from late Middle English.
wiktionary
From Middle English in, inn, from Old English inn(“a dwelling, house, chamber, lodging”); akin to Icelandic inni(“a dwelling place, home, abode”), Faroese inni(“home”).
etymonline
inn (n.)
Old English inn "lodging, dwelling, house," probably from inne (adv.) "inside, within" (see in). Meaning "public house with lodging" is perhaps by c. 1200, certainly by c. 1400. Meaning "lodging house or residence for students" is attested from early 13c. in Anglo-Latin, now obsolete except in names of buildings that were so used (such as Inns of Court, mid-15c.).
