You can long-tap on a actively roaming Dragon to view its Stamina Capacity and Current Stamina. You can also tap on the "?" circular button to view its merge chain, where the information of all the Dragons in the same merge chain that you have discovered is arranged.
When a Dragon Whelp is first hatched, it has some bonus Stamina, which persists until all Stamina is spent, at which only up to the Stamina Capacity is recovered.
The moment Dragons start to work on Build Sites, they use up one Stamina immediately. Thus, it is not recommended to disturb* them while they are building as it lets the Stamina spent go to waste. *Tapping the Dragons or the Build Site
While Trophy Dragons have more Stamina then the other types of Dragons, Midas Ducks is the exception, where it can only reach a maximum of 4 Stamina at Level 10, the lowest amount of Stamina in the game.
The Ghastly Dragons has the most amount of Stamina in the game, topping at 23 at Level 10.