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.).
c. 1300 (late 13c. as a surname), "one who has charge of some person or thing, warden," agent noun from keep (v.). Sense of "one who carries on some business" is from mid-15c. Sporting sense (originally cricket) is from 1744. Meaning "something (or someone) worth keeping" is attested by 1999. Brother's keeper is from Genesis iv.9.