Inchoative

Inchoative is a term used for verbs whose meanings can be paraphrased as 'TO BEGIN TO...' (e.g. inflame and depopulate) or verbs which express the beginning of a state or process, like harden (become hard), die (become dead) or break. The term is also used in explicating the ambiguity of John will eat his lunch in an hour: the inchoative reading is the one in which it will take an hour before John is to eat his lunch.

Link
Utrecht Lexicon of Linguistics