Much like every Pokemon Game since very first ones ever created, there are a number of characters within the game that would like to trade with you. Almost all of these Pokemon you trade for will have a nickname, and most will also be holding an item. Some Pokemon trades are most worth it then others. There are exactly seven In-Game Trades a player can make.
In-Game Trades
Machop - Route 2: In the Route 2 Pokemon Center, there is also a trainer wanting to make a trade with you. They are hoping to trade their Machop, and they're seeking a Spearow in return. The Machop is at Level 9 and nicknamed Macho, also holding an X Attack. This Machop is greatly useful for your First Trial.
Bounsweet - Route 5: Within the Route 5 Pokemon Center is another trainer looking for a trade; they want to trade their Bounsweet for a Lilliup. This Bonsweet comes at Level 16 and is nicknamed Bouncee, also holding the Bright Powder.
Poliwhirl - Konikoni City: Within the Konikoni City Pokemon Center is a trainer who can decide what to evolve their Poliwhirl into, and thus would like to trade it to you. All she is seeking in return is a Zubat. The Poliwhirl is at Level 22 and nicknamed Whirly, also holding a Waterium Z.
Happiny - Malie City: Within the Sushi High Roller in Malie City is a trainer that would like to trade you her Happiny for a Pancham. This Happiny is at Level 27 and nicknamed Happini, but isn't holding any item.
Graveler/Golem - Tapu Village: Within the Pokemon Center in Tapu Village is a man with a theory about how two certain Pokemon only evolve by being traded. He will offer you his Graveler for Haunter, which will end up evolving into Golem after it has been traded. The Golem is at Level 32 and is nicknamed Veler, also holding Rockium Z.
Steenee - Seafolk Village: In Seafolk Village is a trainer staring at that sea that would like to trade you her Steenee for a Granbull. This Steenee is at Level 43 and nicknamed Stena, also holding Grassium Z. This Steenee also has very high Special Defense IVs.
Talonflame - Poni Gauntlet: Just before The Battle Tree entrance on Poni Gauntlet is a man seeking to trade you his Talonflame for a Bewear, believing it will help him when he takes on the Battle Tree. This Talonflame is at Level 43 and is nicknamed Talo, also holding the Firium Z. This specific Talonflame also has its Hidden Ability of Gale Wings.