In older writings, from about the 600s to the 1600s, nim, nime, or nym was one form of the verb meaning 'to take', and its many related senses. It comes from the West Germanic root nem-, and in the days of Old and Middle English nim and the Scandinavian-rooted tacan battled it out over which would be the English verb of choice. Obviously, 'take' eventually won out.
In Old English niman meant to take, accept, receive, grasp, pick up, catch, or steal. At that point it was fully conjugable, and nim was only the imperative, first person, and second person subjunctive forms (If you would like to see the full set of conjugations, I recommend this site). Over time any number of conjugations and alternate spelling were used, including a number of nom, noom, and nome variants. Forms such as neme and nomen might easily be confused by the casual reader as variants of 'name' or Latin 'nomen', which is why there are so very few casual readers of Old English.
The use of nim decreased precipitously during the 1500s, and by the early 1600s the primary remaining usage was in the sense of 'to steal'. At this time is was also used as a noun; a 'nim' was thief. This too has dropped out of usage, and I am not aware of any words in current usage that derive from the root nim.
A particularly well-read person might also find nim used as a name for the Indian neem or margosa tree.
References:
The University of Michigan Middle English Dictionary
Etymology online
The Oxford English Dictionary