Easter Eggs

There's a few game features that were implemented by creators but not revealed by them, that player community calls Easter Eggs.

Pikachu
Pikachu is the most favoured and iconic Pokémon in game. But there are also few less noticeable features in game related to Pikachu, such as:
 * Its silhouette is in Pokémon Collection button White Button Pokemon.png in Main Menu Button Main Menu.png.
 * Its image is on PokéCoin icon PokeCoin.png.
 * It has a lineup of various costumes for certain events in game.
 * Along with extra-small Rattata and extra-large Magikarp, for catching Pikachu there is special medal that Trainer can achieve.

Starter Pikachu
One of the most well-known easter eggs in Pokémon GO is the possibility of getting a Pikachu as a Starter Pokémon, just like Ash Ketchum in the anime.

At the start of your journey, Professor Willow gives new player an introduction to the game and Pokémon, then new trainer is given the task to capture a Starter. The three starters from Kanto region appears - Bulbasaur, Charmander, and Squirtle.

If the players wants Pikachu, then they have to walk away from these three to make them disappear and re-spawn again next to the trainer at his current location. Players have to repeat this action few times until Pikachu show up along with the previous three Starter Pokémon.

Cry of Pikachu
If a Pokémon is tapped while looking at its summary page, it performs its attack animation and its cry can be heard. Pikachu is the only Pokémon that says its name, just as it does in the anime series.

Buddy Pikachu
Initially when a Pikachu is assigned as a Buddy Pokémon, it will show up on the ground beside the trainer. However, if trainer walks distance of 10 km or more, the Pikachu will appear on top of the trainer's shoulder. Similar case happens to be with Eevee as Buddy Pokémon.

This is most likely a reference to Ash's Pikachu always being on his shoulder.

Evolution
The most well-known easter egg is the Eeveelution easter egg. In the anime episode "The Battling Eevee Brothers", there are four brothers each with a different Eeveelution.

Mikey, the youngest has the base form, Eevee, who is pressured by his brothers to evolve Eevee to one of the different forms. Sparky has Jolteon, Rainer has Vaporeon, and Pyro has Flareon.

In Pokémon GO, the trainer can nickname their Eevee with the three older brothers' name to get the corresponding Eeveelution. This Easter Egg was confirmed by Niantic CEO at the 2016 San Diego Comic Con. However, it can only be done once for each eeveelution.

This naming trick has been been extended to include the Johto-region Eeveelutions. In the animates series, there are five sisters called the Kimono Girls who each have a different Eeveelution — the most notable being Tamao's Umbreon and Sakura's Espeon.

Therefore naming Eevee one of following names will result in respective "eeveelutions":

Buddy Eevee
Similarly to Pikachu, when Eevee is assigned as a Buddy Pokémon, it will initially show up on the ground next to the trainer. However, once Trainer walks with it at least 10 km, the Eevee will appear on top of the trainer's right shoulder.

Pester Ball colors
Pester Ball is a lesser known Poké Ball that made its appearance only within Pokémon Snap. In the game, the Poké Ball has the same effect as Repel which helps the photographer take photos of Pokémon. It is also special because it has four different colours, Red, Orange, Blue, and Purple. The center of the Poké Ball is purple, then, going clockwise, the outer layer is divided into three equal parts of Orange, Red, and Blue. This Easter Egg will appear in the app by holding down the Poké Ball icon and then sliding your finger to each of the four icons of the menus, without lifting your finger. A coloured ring will temporary appear showing Orange for Pokémon, Red for Pokédex, Blue for Items, and Purple for Shop.

Also, since Pester Ball was used in Pokémon Snap to reveal a disguised Ditto, there are various rumours about the connection between this Easter Egg and Ditto.

Pokémon Eggs like butter
Also in the Egg section, there are players who have encountered a weird quote saying "Hatch this egg by feeding it butter. It likes all kinds of butter, every kind. The best kind." when entered bugged detail screen of specific egg. This could be a reference to Alice in Wonderland or it could imply an item that is yet to be introduced that helps with egg hatching.