MrSharp said:
...Is there a term for having your firearm not concealed but not completely in the open?
No, there is no term for that.
There are really two dimensions to the question: (1) social; and (2) legal.
I. Social Issues.
The social issues with concealed and open carry revolve around the reaction of onlookers to the fact that you are obviously carrying a gun. In some places, it's not an issue. In other places various member of the public will find the fact that you're obviously armed to be very disturbing. (Whether or not that matters to you is another question.) And there is the theory that being obviously armed is a deterrent to criminals.
In any case, if the gun is only partially concealed the fact that you are armed will be apparent to at least some others and probably have the same social impact, if any, as a gun that is not concealed at all.
Legal Issues
Where open carry and concealed carry are both legal without any permit, partial concealment probably won't matter one way or another.
Where open carry and/or concealed carry is legal with a permit, and if you have the appropriate permit, partial concealment probably won't matter one way or another.
Where open carry is legal without a permit, concealed carry is legal with a permit, and if you don't have the appropriate permit, you will now need to do some serious legal research. It's possible that statutes or court decisions in the jurisdiction have clarified whether or to what extent partial concealment is either open carry or concealed carry. If those statutes or court decisions have defined your partial concealment to be open carry, you're fine. If those statutes or court decisions have defined your partial concealment to be concealed carry, since you lack the necessary permit you're violating the law. And if there are no statutes of court decisions clarifying the matter, it's a crap shoot.
Sometimes things can get complicated. For example, in Arizona, someone with a permit may carry concealed in a place which serves alcohol as long as it's not posted and he doesn't drink. But while open carry is generally legal in Arizona, open carry in a place serving alcohol is not. If your partial concealment is considered open carry, you need to stay out of places which serve alcohol.
Another wrinkle, in some States in which open carry is not legal but concealed carry is the law specifically provides brief, accidental exposure of a concealed gun is okay. I doubt that would apply to a gun which is being carried partially or poorly concealed.