Potions are made by alchemists all over the Desert Realm. Some are fairly common, while others are very hard to find.
Identifying a Potion:
Most other alchemists will be able to identify a potion unless it is a really weird potion that someone made and isn't on the list. But even then they MAY be able to figure out what it probably does.
As for other people figuring out a potion, it is possible that if you've used a potion before, that you may be able to identify it from its scent. But if you're never had it before, then no. For this reason you may want to keep track of which potions you've used before, because you can probably identify them from odor and color.
The reagents listed do not necessarily need to be the only ones. You are free to make up other reagents as you wish, so long as they aren't something specific from another game system. It is assumed that other reagents will be used, and if you are playing an Alchemist character that you will not necessarily need to list them all when you are making your potion. The reagents listed here are primarily done to show the value of the potion (or lack of it) by specifying the ingredients as common or rare.
The reagents used in potions are not the important part, and more data regarding the actual creation of potions will be made available in the Treatise On Magic In The Desert Realm. The most important factor is the ability to Embue Magic into a potion. All potions using magic to perform their effects require this, and will not function without it (regardless of their reagents). In fact, most potions that require magic are dangerous until magic has been embued upon them, and are actually poisonous.