This plant is a rose geranium related however distantly to geraniums like these below. While potted geraniums with large blooms are still popular the "rose" geraniums in pots or as small trees and shrubs seem to be out of fashion possibly because their greatest strength is also their weakness; they grow quickly from cuttings but hence need pruning.
And why call it a rose geranium?
If you have one pick up a leaf and snap it open. In the rose geraniums and other members of the pelargonium group there are essential oils and the leaves can smell of mint or rose or other aromas.
I was going to get rid or prune back drasticly most of my geraniums but I'm going to try to sell or swap my cuttings and prunings.
Going back to the top image this one has gone "leggy". I however don't want the long stem look. I'm trying to slowly and gently coax this one into a better shape with cuttings here and there.
If anyone wants some cuttings to start their own plants let me know. I'ld love to swap for some extra empty pots!