Learn English – What’s the word for asking someone to deliver their promise

There are a few words for this... I think the one that best fits your description is "yes-man":

a person (especially a man) who agrees with everything that someone says : a person who supports the opinions or ideas of someone else in order to earn that person's approval

The first one to come to mind was "toady", which has the added benefit of being a noun and a verb:

Noun: a person who flatters and ingratiates himself or herself in a servile way; sycophant

Verb: to fawn on and flatter (someone)

Sycophant is also a good word:

a person who seeks favor by flattering people of wealth or influence; parasite; toady

There are a bunch of other options, though, including "flunky":

"Speaking for" someone and "speaking on behalf of" someone mean essentially the same thing, with one fairly major difference. To really be "speaking on behalf" of someone, that someone needs to consent to you doing so. So if someone says they are "speaking on behalf of" John, they are implying that John knows what they are doing and approves of it. You can "speak for" someone without their consent, as in your example between you and John. So "speaking for" can have a negative connotation, but does not necessarily. "Speaking on behalf of" does not have a negative connotation, unless you have reason to believe that they are not telling the truth.