Yep—after enough story progression, you can talk to Charmander and visit Professor Tangrowth together, who will give you the Ditto flag, which lets you designate a house as Ditto's house. Since you've already built a house, the option should be available soon if not already unlocked. You can put the Ditto flag in front of your vacant house, or choose any house that's already occupied if you want to have a roommate.
Afterwards, you can create more Ditto flags with 1 Sturdy Stick, 1 Twine, and 1 Leppa berry.
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