This is easy. Paste the new operator's logo over the existing
livery until they get a new paint job (in this case, the government
livery). Transdev Melbourne did exactly that when they took over
from multiple operators.
Private operators tend to favour having their own liveries as it
improves their brand visibility. When New South Wales (Sydney)
government decided to adopt a unified government livery it faced
fierce resistance from the existing private operators.
Precisely why Transperth lagi best. The only indication of the
operator's identity is a small sticker in the window that says
"This Transperth bus service is proudly operated by Path
Transit/Swan Transit/Transdev". Since the private contractors do
not own the fleet, they do not get to put their own liveries on the
vehicles.
On the same note, I am in favour of nationalising the entire
public bus fleet in Singapore and adopting Transitlink
(LTA) livery for them. Even if SBS and SMB are operating and
maintaining the buses, they still do not get to paint their logo on
the vehicles and can only put a sticker in the window for
differentiation.