At one point you could customize the outpost ship's deployed station. This has disappeared. The refuel depot component is available for stations tho (where it is pointless). Is there a way to customize outpost stations ?
Additionally if you name a space station design Outpost the design becomes undeletable (and you cannot change its name) yet does not affect deployed outpost design.

There was some difficulty when we made the Space Station use the same hull as the Outpost, where you could edit the Outpost (which is not very useful) but not the Space Station. The short-term fix was to hide the Outpost design. It's not useful to be able to edit the Outpost itself, otherwise it can't do the job for which it is intended (range increase); it would be nice to be able to create alternate designs for the Outpost Transport to carry (to deliver prefab space stations), but that would mean there would have to be some means by which you can choose which payload to carry when you build an Outpost Transport. Which at the moment is more trouble than the feature is really worth.

The weirdness resulting from naming another design "Outpost" is almost certainly due to the fact that a lot of the logic in the game keys off the actual display name of the unit instead of an internal identifier, which is going to cause us all manner of headaches in the future.

With solar panels improvement, though, outposts gain a bit more functionality. Low priority I know, but being able to customize them again would be useful.

It's something we'd like to do, but there are higher priorities right now.