Unlike her ex-husband, Hank Pym -- who's assumed a number of different guises over the years, such as Ant-Man, Giant-Man, Goliath, and Yellowjacket -- Janet Van Dyne has consistently stuck with the 'Wasp' identity during the entire time that she's been a superhero. She first adopted it in Tales to Astonish Vol. 1 #44
(March, 1963), and up until her apparent death in Secret Invasion #8 (January, 2009), was the only character to have ever used it.
And, as she shrinks to minuteness, gossamer, dainty wings sprout from Janet's shoulders and tiny, delicate antennae adorn her forehead! The lovely girl has truly become... the Wasp!
Tales to Astonish Vol. 1 #44 (March, 1963)
In Secret Invasion: Requiem #1 (February, 2009) -- shortly after Jan's apparent death -- Hank Pym took over the mantle in her honour, becoming the second Wasp. He subsequently reverted to his Giant-Man guise in Avengers Academy #7 (February, 2011).
HANK PYM: Over the years, I've reinvented myself as a super hero so many times... Ant-Man, Giant-Man, Goliath, Yellowjacket... always trying to carve out a legacy for myself. But now...? ...I can think of nothing more appropriate... than taking up someone else's mantle. The greatest hero I've ever known. Call me... the Wasp!
Secret Invasion: Requiem #1 (February, 2009)
In Avengers Vol. 4 #32 (December, 2012), it was revealed that Jan hadn't actually died, but was instead transported to the Microverse. She was eventually rescued by the Avengers, after summoning them with a distress signal. Shortly after that, she resumed her costumed identity as the Wasp.
Uncanny Avengers Vol. 1 #5 (May, 2013)
Some time later, in Free Comic Book Day Vol. 2016 Civil War II (May, 2016), Nadia Van Dyne constructed her own costume out of spare parts she found in Hank Pym's home, and became the third (and currently, final) Wasp in the Earth-616 reality.
NADIA VAN DYNE: The doctor would have taken pity on me in that moment, I know he would have. He would have forgiven me for what I felt forced to do. For laying claim to his laboratory... and to his life's work. I believe the American phrase is "Kid in a candy store." It was more... astonishing than I'd ever dared imagine. World-changing theories in every notebook. Half-finished miracles on every shelf. At my fingertips, everything I could possibly need to finish remaking myself into the girl I'd always longed to become. In Russian, "Oca." In English... the Wasp.
Free Comic Book Day Vol. 2016 Civil War II (May, 2016)
Nadia met Jan in All-New, All-Different Avengers #10 (August, 2016), who effectively gave her blessing for both of them to use the 'Wasp' name concurrently a couple of issues later.
NADIA VAN DYNE: That... was... amazing! Jan, I just hung out with the President! Of the United States! Look at all this cool stuff he gave me!
JANET VAN DYNE: You did him a solid, Nadia. And you were great today. You certainly taught me a thing or two about defusing Microverse bombs. It looks like two Wasps are better than one.
All-New, All-Different Avengers #12 (September, 2016)