What is the word for finishing/doing a dare?

As with any commitment, you can honour a dare.

fulfil (an obligation) or keep (an agreement):

In US English there is a phrase take a dare that means

be dared to do something and attempt it

There are numerous references in literature with this meaning, as the citations behind this ngram reflect. The sense is to undertake a dare.

Unfortunately, to some people the phrase also may mean

be dared to do something and not attempt it [emphasis added]

The ngram also reflects that. The sense is to put up with [to take it].

Context is everything.

I might say that the person has completed the dare, in the same way that one might complete any other assignment:

1 : to bring to an end and especially into a perfected state <complete a painting>

People typically "follow through" their dares (and threats!)

definition of the idiomatic phrase: "follow through (with something)" and "follow something through":

to complete an activity, doing what was promised.

One accepts a dare when he agrees to undertake a challenge or (more weakly) a mission, so the idea that a dare is ever finished, completed does not make sense.