I think i had this and if it's the same thing then you're right Evert it's from the Gesnereaceae. I think it's a lesser known Streptocarpus. Can't for the life of me think of the species name though. There are a couple that are rather similar. The one I had was something issima. If so, it loves a drink and grows quite rapidly into a waterfall of a plant. The flowers are bluey violet tiny editions of a cape primrose. Very attractive when well grown, but mine got very straggly and then sulked because i couldn't work out just what it wanted (probably a greenhouse).
I wasn't quite sure if what I am seeing is hairy or shiny. You are right, I don't know of a hairy Peperomia either, but then I am not too familiar with that genus.
Streptocarpella is very hairy, at least the one I have growing here (don't know which species). Can't tell from the picture if the leaves on your plant are opposite or alternate. In Streptocarpella they would have to be opposite, in Peperomia alternate.
I'm sure you will have an answer the minute it flowers!
The Streptocarpus i was trying to remember is glandulosissima. From what i can recall, your photo looks very like the plant i had of this. No doubt all will be revealed when it flowers. Any sign of that yet?