Well, Partridge has this to say about nick the noun:

"(See entry at nias.) 2. The female pudend: low coll.; C. 18-20; ob. Robertson of Struan, who, like G A Stevens, tended to obscenity. --3. Abbr. Old Nick (q.v.), the devil: coll.; 1785 (EDD) --4. Only in nick and froth, q.v. --5. (the nick.) The proper, the fashionable, thing or behavior: ca. 1788-1800. Lord R Seymour in Murray's Magazine, vol. 1, OED. --6. (the nick.) Good physical condition or health; almost always in the nick: late C. 19-20. C J Dennis. --7. See nick, on the, --8. (the nick.) A prison ('Stuart Wood', 1932); a police-station (Charles E Leach, 1933): c. (from 1919). Prob. ex sense 3 of the v., but imm. ex military s. (ca. 1910), the guard-room, detention-cells (F & Gibbons). --9. See nicks."

And the verb:

"To cheat, defraud (of): coll.; late C. 16-20; very ob. Taylor the Water Poet. (OED) --2. To catch, esp. unawares: from ca. 1620. Fletcher & Massiger. In C. 20, occ. to get hold of, as in Galsworthy, The White Monkey, 1924, 'Wait here, darling; I'll nick a rickshaw.' --3. Hence, in C. 19-20, to arrest: low s. or perhaps c. The Spirit of the Public Journals, 1806, 'He ... stands a chance of getting nicked, because he was found in bad company,' OED. --4. To steal; purloin: 1826 (EDD); 1869, Temple Bar, 'I bolted in and nicked a nice silver pot': c > , by 1880, low s. --5. To in-dent a beer can: C. 17-18: either cool. or, more prob., SE So too the vbl.n. --6. To copulate with: low coll.: C 18-20, ob. --7. V.i. to drink heartily: Scots s.; late C. 18-19. Jamieson."

So, it seems the noun came from the verb. And what a lot of meanings for nick.