What meditation do you do?

[CrystalSong]

Silence is learned. It takes training the mind that meditation isn't the appropriate time to be busy thinking - just as one would gently train a child to not interrupt when others are talking.

Yes when a thought is noticed then just release it unfinished. Trying to 'stop' it requires too much vigilance and the mind will turn into a dog chasing its own tail. So instead when a thought is noticed do something like 'oh a thought, then don't be the thought, don't become the thinker of the thought - give it no more importance than the passing random whispers in a theater before the lights dim. Don't eves drop on the thoughts and get caught in the thoughts or have opinions about the thoughts.

So it's not a 'letting it finish' or 'stopping the thought' it's a Not Being the Thinker of the thought and just noticing thought exists without us being the thinker of the thought.
We can also slowly train our selves to make a head space in which thoughts are random happenings and controllable and instead after some random thoughts, like an audience settling in for a performance as the lights dim and stopping chattering and turning its focus to the stage, we can also focus ourselves and pay attention to the that which happens inside us which is not thought.