I wouldn't use it. Have you heard of the book A Kestral for a Knave? It was adapted into a film called Kes. The story is pretty sad. The title is from the hunting birds that were associated with class.
Gerfalcon or a Gyrfalcon (esp. the male, also called tercel) was for the king.
Falcon or tercel gentle for a prince.
Falcon of the rock for a duke.
Peregrine or a bluehawk for an earl.
Bastard hawk for a baron.
Saker for a knight.
Lanner for a squire.
Merlin for a lady.
Hobby for a young man.
Goshawk for a yeoman.
Sparrow hawk for a priest.
Musket for a holy-water clerk.
Kestrel for a knave and a servant.
So basically a kestral is for someone of very low class. I wouldn't use the name because of this. There are bird names with nicer associations, such as nightingale.