Gentian is one of the most common bittering agents used in cocktail ingredients. It is a dominant flavor in Angostura and other aromatic bitters, a prime flavor in gentian liqueurs including Suze, Aveze, and Saler's, and it is included in many other bitter liqueurs and fortified wines.
According the the United States FDA [link]:
Gentian rhizome & roots (Gentiana lutea L) is allowable as a natural flavoring
Gentian, stemless - (Gentiana acaulis L) is allowable in alcoholic beverages only
Stemless gentian is the blue-purple flower type of gentian [link], while gentiana lutea is yellow gentian [link]. Both of these types of gentian are commonly used in fortified wines and bitter liqueurs.
Note there is also a dye/medicine called gentian violet [link] but it is not derived from gentian plants. Its chemical name is methylrosaniline chloride. We do not address this chemical here.
Gentian has been used for many years as medicine to treat digestion/stomach-related issues.
According to RXList [link], "The highly toxic white hellebore (Veratrum album) can be misidentified as gentian and has caused accidental poisoning when used in homemade preparations."
There are some concerns about taking gentian if you are taking blood pressure medications or will have surgery [link].