Officer Jennies are not one being.
An Officer Jenny in Ever Grande City mentioned that she had a Blastoise and she attempted to use it against the Team Rocket trio , who were attempting to steal the sacred flame of Moltres.
In the Best Wishes series , Jenny recieves a new design and now uses Herdier and Swanna due to the fact that Growlithe aren't native to Unova.
Swanna was used twice in the anime, the first in The Lost World of Gothitelle. However, Nurse Joy stopped Jenny because Blastoise could accidently put out the firewhere it tried to use Defog to clear the fog off Skyarrow Bridgebut failed.