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.