Tweetot's name and (non-shiny) color scheme could be in reference to Twitter, a popular social media site that features a blue, ambiguous bird as its mascot. Posts and reblogs on Twitter are called Tweets and Retweets, respectively.
Tweetot and its evolution are one of only three Psychic/Fairy Fakemon featured in the Rikoto Regional Dex, the other being Felove.
However, Felove's type combination is Fairy/Psychic which is in reverse.
Tweetot shares the same name as an old Fakemon made by WaterTrainer that was meant to be a Pre-Evolution for Chatot.
Tweetot was a Flying type instead of a Fairy type in earlier versions of the game.
Tweetot is based on a bird. Tweetot's shiny color scheme of pink could refer to Valentine's Day, a day known for birds, music, candy, cards and romance. It is also usually symbolized with colors like red, purple, and pink.