How can I make milk cocoa powder so it does not stick to the top and bottom?

I do not think your problem is an emulsifier that you are missing, I think it's just basic temperature and technique 'issues'.

Firstly, you will get a better result if you use a liquid chocolate syrup. It's like adding granulated sugar to an iced coffee - it will sweeten the cold liquid a bit, but most of the grains will just get wet and clump together at the bottom and not mix together. That's why using a simple syrup is a better idea, because the solid elements (sugar) have already been incorporated into a liquid form so the cold temperature won't be a detriment to mixing.

However, if you really want to keep using (or not waste) your existing cocoa, you have a few options. You can make a slurry of the cocoa powder. Get a container that can be sealed well and add maybe a teaspoon of the cocoa mix to 3 or 4 tablespoons of milk and shake it vigorously. Once it is well mixed, you can add more cocoa, and more milk as needed to keep it totally liquid. After it is fully incorporated, stir it into the rest of your milk and it should mix completely.

This other method may not work for cold milk, but it is how I make smooth hot cocoa without having to make a slurry. I take a good quality cocoa and put it in a small bowl and then add granulated sugar - the ratio isn't vital (and I like a sweet, very chocolatey cocoa), but it does have to be enough sugar to fully incorporate with the smooth, powdery cocoa. Basically I am looking to use the grains of sugar to break up the potential clumps of cocoa by having the mixture as thoroughly incorporated as possible, and then stirring very thoroughly as well. I prefer glass mugs so that I can see that I've gotten all that's fallen to the bottom.

I hope this helps.