The design and name of each and every Pokémon is based off of something or another. For some this is obvious and others not so much. In the case of Pidgeot it is fairly obvious, although there are some things about it that don't quite make a whole lot of sense to me. I'll go on to explain why I think so.
Despite its name, appearance, and behavior Pidgeot seems more like a bird of prey rather than a pigeon. In fact, Pidove is more like a pigeon than Pidgeot is. Pidgeot is more like an eagle or a falcon. Its shiny form colors are even quite similar to that of a golden eagle. Despite all that though I still think Pidgeot is pretty cool. It is interesting to note that the markings by its eyes bear a striking resemblance to the markings seen on the Sun/Sky Gods Ra and Horus of Egyptian Mythology. Pidgeot's whole head kinda looks similar to the Gods' as well. Coincidence?
Pidgeot's name is pretty easy to figure out, but I also wonder why it, and its previous evolutions, were given such names. Both its English (Pidgeot) and Japanese (Pigeot) names come from a combination of the words "pigeon" and "jet", likely a reference to its faster-than-the-speed-of-sound speed. While I sometimes question the use of "pigeon", I think "jet" definitely works for this Pokémon. I guess I can't really complain though because I really do like Pidgeot's name. I have issues.