This comes up every now and again and the following are worth pointing out: 1. Nobody ever agrees on the line names. 2. The orange corporate branding is now quite well-established and changing it would break some of that hard earned branding 3. It already effectively is operated in lines, and generally referred to as such (North London Line, East London Line, Goblin, etc).
Providing a separate map isn't a good idea - the whole point of Overground is to intercept journeys from radial lines to avoid changing via Zone 1. Also different shades of Orange isn't helpful as it slows down interpretation of the map. The Overground needs to be shown in the context of the London Rail connections map, and therefore needs a clear identity in that display.
I'd personally use a Letter for Each line and then numbers for the branches. So Stratford-Richmond would be route N1, Stratford-Clapham route N2, Euston-Watford W1, Highbury and Islington-New Cross E1, etc.