Leenia, "bare infinitive" is the common term for a verb in an infinitive construction without "to." Linguists consider verbs following modals (can, will, etc) infinitive forms as well, as they don't carry tense or aspect. There is a list of other uses of the bare infinitive here:

https://www.englishgrammar.org/bare-infinitive/

The grammar police won't arrest you for calling them all idioms, of course, but usually the term applies to idiosyncratic, nonproductive forms: If a new verb comes into the language, however, it will be used with causative "have" in the bare infinitive form. "They had him schmerk"; "They bade her schmerk"; "They would do anything except schmerk" etc.

Tattie, in northern West Virginia (and probably elsewhere nearby) "needs washed" is a common form that invariably throws visitors for a loop. My former wife, who was from here, when asked, "Why do you folks say 'something needs washed,'" replied, quite sensibly, "Because it's dirty?" Settlers in this area call themselves Scots-Irish, and there may be something to that.