In A Midsummer Night's Dream, Puck is called a hobgoblin, yet can he be classified as a mischievous fairy?
Puck is called many things in this play. The reference to "Hobgoblin" comes in Act II, scene i, when Puck meets one of Titania's fairies in a spot that both Titania and Oberon are claiming possession of. This fairy does not seem to be very friendly to Puck, so the words that he/she speaks against Puck are simply this one character's opinion, but also reflect the mercurial nature of who and what, exactly, Puck is.
Here's the text spoken by the First Fairy, abridged to show the different names used to refer to Puck:
Either I mistake your shape and making quite,
Or else you are that shrewd and knavish sprite
Called Robin Goodfellow. . . .
Those that "Hobgoblin" call you, and "sweet Puck"...
This fairy, even though he/she is not on Oberon's team, and as Titania's fairy has no reason to particularly like Puck, calls him "shrewd," "knavish," a "sprite," "Hobgoblin," and "sweet Puck," all which conjure up some different images.
Certainly Puck admits in his next speech to being mischievous (as you describe him). Puck says:
I am that merry wanderer of the night.
I jest to Oberon and make him smile...
Puck goes on to describe some of the tricks he has played on unsuspecting humans. So, yes, certainly, among other things, Puck can be considered a mischievous fairy.
For more about Puck and the fairy world of Shakespeare's s day, please see the links below.