There really is nothing in Confluence to define a space owner. If you want to set up something like this it will be a bit of a manual job. I would go to Space tools -> Look and Feel ->Layout.
Edit the Page Layout decorator to put the space owner somewhere on the page. This will have it show up on every page in the space. You can makes these changes different per space.
Two other possibilities,
1) Create a new user group (for example, new group name is "Owner" so the new group's name displays as "Spacename-Owner"
2) Put the space owner in the new group
3) Use the User List macro on a page to display the members in "Spacename-Owner" group.
This should display a gray bar with "Group: Spacename-Owner" in it, followed by a list with the name of the owner in it.
Second option,
Use the User Profile macro on a page and specify the space owner.
This should display the user's name and email, picture, phone, position, department and location if they are filled out in the user's Confluence profile.
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