A noise
Incorrect : Don't make noise.
Correct : Don't make a noise.
Note: "Noise' can be both countable and uncountable. As a countable noun, it can be both singular and plural. In the expression above, it is a singular countable noun. So the article 'a' before it is a must. You can however say:
The engine is making funny noises. (plural)
There's so much noise in this restaurant. (uncountable)
Like “make a noise', we can also say:
He made a mistake.
We made an attempt to enter the room.
They have made an experiment.
He made a fortune.