We each have our "offices" but we don't have cute names for them. My husband's doubles as a guest bedroom, but he doesn't use his as much as I use mine. I work in mine, but also spend time there doing other things, including sleeping if DH snores or I'm just feeling restless.
The best thing about these spaces to me is that we each have a place to put our "things." Anything he wants to display that I'm dubious about (sports paraphernalia, college mementoes, tacky stuff in general haha) I can just say "let's put that up in your office." He can store all his old train sets and baseball cards and obsolete (although he won't admit it) photography equipment in the closet. If he leaves junk lying around the house I can just put it in his office for him to deal with when he gets around to it.
I have a large walk-in closet in my office where I can store Christmas gifts (it's blessedly empty right now!), wrapping paper and gift bags, birthday party supplies, the kids' art supplies, and other things that don't have a home elsewhere in the house. There's plenty of room because all my clothes are in my bedroom closet. I also have a "keepsake" plastic bin for each of the kids and one for the family in general where I put the kids artwork, report cards, some birthday cards, awards and certificates, some of their baby clothes, and other memorabilia. The family one is full of vacation mementoes and other stuff I want to keep.
I am sort of envious of couples who thrive on closeness, but we're just wired differently. Our relationship thrives BECAUSE we have our separate spaces to retreat to when we feel the need.