While you technically own a Rotom on your trainer’s phone and have a Rotom-controlled Pokédex, you do not have its habitat or data. However, you can find one and change its forms in the game.
Rotom is a rare encounter in the Wild Area. The weather plays a huge part in obtaining Rotom—you need it to be raining or thundering. Travel to the Lake of Outrage and surf through with your Rotom Bike. Soon, you will see a land with a patch of grass and a den. There are other types of Pokémon, including Seismitoad and Araquanid, here. Rotom will have an overworld sprite, and once you see it, go ahead and run to it.
Rotom Catalog Location
To find the Rotom Catalog, you will need to have access to Wyndon. At the Pokémon Center, walk or ride your bike to the right, where there will be many townhouses. Keep going up until you see the second-to-last house and enter it. You will see a male League Staff member. Talk to him, and he will talk to you about how Rotom likes to jump into different motors. You will be given the chance to battle him. Say yes, and you will begin the battle against his three Rotoms. They are around level 30, and the forms you will fight are the lawnmower, washing machine, and microwave oven.
After defeating the League Staff member, he will give you the Rotom Catalogue. After capturing a Rotom, you are free to change the forms of your Rotom, whether for fun or for competitive battling.