Dunno about a dozen teams, but the official ones were "The Sparrows" formed in 1957. "The Redskins" took over in 1958 and "The Pelicans" were formed in 1959. There were, however, other duo's and such flying the JP.
"The Pelicans" carried on through to 1973. During which time they spent 1964 displaying with "The Yellowjacks" in their Gnats, and became the RAF's official team. "The Red Arrows" were in fact lurking in the background until they took over the mantle of the official team in 1974(ish).