What is the P in 'nope' called?

Brief answer:

Nope is a variant of no (exclamation), usually pronounced as [nəʊp̚] (AmE [noʊp̚].

Merriam Webster says its first known use dates back to 1888; however, according to Wikitionary, it was used for the first time in the 1850s.

The P in nope is epenthetic and the process of adding it is called Epenthesis.

Explanation:

Epenthesis is the pronunciation of an unhistorical sound within a word usually added for articulatory reasons. Consonants and vowels are usually inserted into words for the sake of ease. Epenthesis happens for a variety of reasons, some of them are:

• to prevent adjacent vowels in a hiatus, for instance, idea of is pronounced idearof, with an epenthetic r, in most non-rhotic accents to avoid a hiatus
• another reason is to simplify consonant clusters, for instance, most Indian English speakers pronounce 'school' ischool (breaking the cluster /sk/)
• between a nasal and a fricative (prince-prints merger)

Some sources call it 'excrescence', though the technical and widely used term for this is epenthesis.

Regarding nope, the P represents the closing of lips after saying No. (exclamation).

Suppose someone asked you a question and you said "No". You would usually pause after saying "No" (exclamation) with your lips already positioned to produce a P.

Other examples include yep, yup and welp ('well'). Yep and yup are the variants of 'yeah' ('yes') as an isolated or emphatic utterance (exclamation), with P representing closing of the lips, creating an unreleased bilabial stop [p̚].

Spanish does the same with si (meaning: yes). Si → sip.