Is there a name for the verbs that can precede other verbs?

Besides the the term given in the comments the arrangement of verbs shown is referred to as a (verbal) construction or pattern, called "verb + to-infinitive" (ref.), or sometimes "verb + infinitive". This latter way to refer to it still permits to distinguish it from the construction where the verb follows without "to", as then this pattern is referred to as "verb + infinitive without "to" or "verb + bare infinitive". (There is but a few of these verbs, the most important ones being the modals; the use of the infinitive without "to" is characteristic of every instance of use of modals. (ref.))