Nope.
You keep the badge you got when selecting your first PPP, and do not gain another.
The wisdom of Shadowe: Ghostraptor: The Shadowe is wise ...; FFM: Shadowe is no longer wise.
; Techbot_Alpha: Also, what Shadowe said. It seems he is still somewhat wise 
; Bull Throttle: Shadowe was unwise in this instance...; Rock_Powerfist: in this instance Shadowe is wise.; Techbot_Alpha: Shadowe is very wise *nods*; Zortel: *Quotable line about Shadowe being wise goes here.*
If you respec your Patron Pool do you get the badge for the one you change to? Like you have Mu Mastery and the Mirage badge but you change to Soul Mastery, would you get the Spider's Kiss badge? (If that's the name
)