Ulster doesn't refer to all of NI, but just one county. That's why they changed their name to UTV in 1993.
The reverse - all of NI is in Ulster, but not all of Ulster is in NI (Cavan, Donegal, and Monaghan being the other three counties). The reason for the name change was the huge viewership in the Republic which they had during the early 1990s - they had more ROI viewers than NI viewers. This fell dramatically after 2000, when a combination of TV3 getting the rights to Granada's (ITV's after 2004) and digital TV (heretofore UTV would have been tuned in to preset 5 on most TVs with analogue cable, but wasn't on the Sky EPG
at all and on UPC was at 110 with TV3 on 103). UTV Ireland was their plan to reverse this.
Likely if they do rebrand, the NI station will be ITV Northern Ireland off air but just "ITV" on air.
The ROI station will likely either stay UTV Ireland, become just UTV, or become ITV Ireland.