How to prevent the cocoa in the hot chocolate from solidifying over time

There really isn't another name for Dutch processed cocoa. You could perhaps look at the ingredients or label and search for some reference to alkalization. Cocoa powder, Dutched or natural, consists of a single ingredient: cocoa. The difference is that Dutched cocoa has an extra step in the manufacturing process.

Normal cocoa powder is created from cocoa beans. These beans are fermented, roasted, shelled, and then ground into a paste known as chocolate liquor. This is roughly 50/50 cocoa butter (fat) and cocoa solids. At this step it is can be molded and sold as unsweetened baking chocolate. To make cocoa powder the liquor is hydraulically pressed to remove ~75% of the fat, and then pulverized into cocoa powder.

Dutched cocoa powder has an extra step before the shelled beans are ground into liquor. They are soaked in an alkaline solution of potassium carbonate.

Dutched cocoa was created in the 19th century by a Dutchman named Coenraad J. van Houten. Van Houten had invented the method of using a hydraulic press to defat chocolate liquor. Hot chocolate in these times would have a fatty greasy scum floating on the top of the beverage. Removing much of the fat prevented this. However, it also made the drink much harsher, acidic, and gave it a much lighter color.

Van Houten's idea was to counteract the cocoa's natural acidity (pH ~5.4) by soaking it in an alkaline solution. This neutralized the acids in the cocoa raising the pH to neutral (7) or higher depending on the duration of the soak. The higher pH also has the added benefit of darkening the cocoa; the higher it goes, the darker it gets.

Now, you might think that mellowing out the cocoa would be undesirable for the flavor. However this has been shown to not be the case. It turns out that the very acidic nature of natural cocoa can actually mask many of the natural undertones of flavor in the chocolate. Chocolate is much like wine and has hundreds of flavors that make up its flavor profile. These include sour, bitter, astringent, fruity, figgy, nutty, floral, smoky, and may more. Dutching only targets the bitter, astringent, sour and fruity undertones allowing the remaining ones to really showcase the chocolate.

There is a bit of misinformation that floats amongst bakers that the pH of the cocoa can affect the leavening of the baked good. Many recipes will actually sternly suggest using either Dutched or natural cocoa depending. This makes sense since leavening is a sort of balancing act that involves both acids and bases. However, it has been experimentally shown that this does not actually occur, and baked goods made with both Dutched and natural cocoa powder showed no differences in leavening.

So to actually address your questions. Again, no there isn't another name for Dutched cocoa, but it can't hurt to check for alkalized verbage. There is (should) also no additional ingredient that would identify a cocoa powder as Dutched. The key property it provides is simply chocolate flavor.

This answer is adapted from the Jan. 1, 2005 Cook's Illustrated review of cocoa powder. Their results showed that without fail Dutched cocoa was voted superior to natural cocoa in every single blind taste test including: pudding, shortbread, devil's food cake, and hot chocolate (which was masked by a sippy-top so reviewers could not see the tell-tale color).

If the cost doesn't make you do a double take (it's not really that expensive considering the quantity). I highly suggest you buy a 1 kg (2.2 lb) bag of Callebaut Cocoa Powder. This was the winner of the blind taste test performed by Cook's Illustrated. I must agree that it will change your baked goods for the better like you would not believe.

Cocoa powder is made by baking the cocoa beans and then removing all the fat from them, then milling the rest to a powder. In fact, semisweet chocolate is a solid sol (a colloid formed from homogenically dispersing solid particles (cocoa dry matter) in a solid (cocoa fat)). What you should add is not water, but fat.

Before you start, you must be aware that cocoa fat has some very special properties. It melts at a very convenient temperature, so it is solid in the air and melts in the mouth. Plus, it has a very special form of crystalline structure, which allows [tempering].1 This means that the substitution won't work for some very specific uses like making Belgian chocolates. For chocolate cake or brownies, the texture will be somewhat off, but not too much, so it should deliver acceptable results for the home cook. The taste will also be different (there is a reason why pure chocolate is so expensive, it only uses real cocoa fat, bars with other fat types like Milka can't compare with the original).

There is also the question of choosing the fat. It should be solid by room temperature. Butter is often used in desserts and has a really good taste, but it doesn't mimic cocoa fat that well, because it isn't a pure fat, it is an emulsion of ~17% water in milkfat. So texturewise, shortening is probably a better choice. You can use either, based on whether texture or aroma is more important for you, plus your camp in the this-type-of-fat-is-bad-for-you debate.

"Semisweet chocolate" is a loose category. I usually count anything with 40% to 60% cocoa mass as "semisweet". So on average, your mixture should contain 50% sugar.

The ratio of cocoa powder to fat is trickier. Luckily, I have a 90% chocolate bar here and can tell you that it contains 55 grams of fat (as given on the package). This means that pure chocolate mass has 60.5% fat. Assuming that your cocoa powder has 15% fat ("weakly de-fatted powder" is my best attempt at literal translation) and that you are using shortening (100% fat), we arrive at a ratio of 54% fat to 46% cocoa powder. You probably don't have to be that exact, especially considering the fact that the fat content of cocoa powder isn't exactly 15%. I'd just go with a 1:1 ratio - easy to measure, and it gives you a bit more cocoa taste.

So the final proportions should be 1 part cocoa powder, 1 part vegetable shortening, and 2 parts sugar. If you feel very mathematically inclined, you can calculate it more exactly for butter and a specific cocoa powder fat content.

It is also important to note that in baking, you can't just throw everything in and mix. Different mixing sequences result in a different air distribution in the batter, which has very important results on the final texture. So don't try to imitate chocolate by mixing above ingredients somehow and then dumping them into the bowl. Your recipe already has a correct technique for combining the ingredients, e. g. by creaming the butter with sugar and then slowly adding the flour. It also describes a technique for adding tempered chocolate to the batter, and this one won't work for a homemade mixture of sugar, cocoa powder and shortening.

To achieve best texture, stick to the recipe's technique for the components. Whatever they say to do with the original butter in the recipe, do it with a mixture of the butter and the chocolate-substituting fat. Use the original sugar amount together with the chocolate. Treat cocoa powder like flour, best mix them in a separate bowl before adding to the rest. Your result won't be exactly like a recipe created with real semisweet chocolate, but only the most discerning eaters will notice it, and most cake eaters are not that discerning.

A last word of caution: throughout the answer, I assume that you have actual cocoa powder (I'd use non-dutched for a stronger choco taste, but this is a matter of personal preference). Instant drink powder like Nesquick doesn't contain much real cocoa and is unsuitable for this kind of substitution (or for any baking purposes).