Fulchia

When you talk to this NPC she will ask you "What do you wish to do?" and will give you two options to choose from, "Nothing In particular" and "Ask for an explanation of Mog Houses".
If you are partied with another character and have the Wings of The Goddess expansion pack installed, your partner could enter your Mog House by simply talking to this NPC (after you enter and select 'Open Mog') which will reveal a third option: "Visit the Mog House of a party member". Select the name whose Mog House you wish to enter.