in nickname, newt, and British dialectal naunt, the -n- belongs to a preceding indefinite article an or possessive pronoun mine.
Other examples of this from Middle English manuscripts include a neilond ("an island," early 13c.), a narawe ("an arrow," c.1400), a nox ("an ox," c.1400), a noke ("an oak," early 15c.), a nappyle ("an apple," early 15c.), a negge ("an egg," 15c.). In 16c., an idiot sometimes became a nidiot, which, with still-common casual pronunciation, became nidget, which, alas, has not survived.
The process also worked in surnames, from oblique cases of Old English at "by, near," e.g. Nock/Nokes/Noaks from atten Oke "by the oak;" Nye from atten ye "near the lowland;" and cf. Nashville.
But it is more common for an English word to lose an -n- to a preceding a: apron, auger, adder, umpire, humble pie, etc. The mathematical use of n for "an indefinite number" is first recorded 1852, in to the nth power.