It looks to me like they combined the EVA 77W "Rainbow" scheme with the standard EVA and UNI schemes. I'm glad they changed the UNI Air logo, as it previously seemed too much like a shipping insignia IMO. I wonder if this livery change presages a EVA change as well, although given the "Rainbow" scheme's existence, I doubt it.
It's also interesting to see that the full-green tail has emerged; as I recall the first EVA 767 briefly had an all-green tail, before they filled in the globe logo with white to make it more distinctive.
Overall, the livery shows more connection with EVA itself, whereas before, the contrasting colors seemed more like how ANA differentiates Air Nippon with its mainline jets. The uniforms also seem to match up with EVA even more as well.
One big purpose of having it around is to count as another carrier when traffic authorities are handed out.
I wonder how their cost structures differ and whether it would also be the low-cost little brother of EVA.
The route authority issue you raised would be the ONLY reason I think to keep a separate branding. Same reason why CI keeps AE around.
I doubt the cost structure is that different if you are talking EVA MD90 vs. UNI MD90 as they have common pilot pool. There are no true low-cost carriers based in Taiwan. As long as China flights frequencies are artificially restricted, Air Asia or Jetstar style bare bones operation and rock bottom fares will not work in Taiwan.