It tended to be the press who went with the abbreviation, particularly newspapers who weren't as hardline-Unionist in ethos. I remember the Belfast Telegraph carrying listings for "UTV", while one local paper used to call the station "Six-County" TV, quotation marks included. Likewise, the News Letter remains partial to references to "Ulster Television", even in a post-1993 context.
The 1970s on-air use of UTV, from the evidence I've read and seen, mirrored the 1990s to an extent; adopting the abbreviation on the evening news programme and presentation elements in tandem with Ulster Television, without going the whole hog of a comprehensive 1993-style rebrand with one coherent brand name.
By the end of the 1970s, that phase of using UTV on-air seemed to pass: UTV Reports morphed into Good Evening Ulster at the start of 1979; and I've yet to come across off-air broadcast material created by the company from the 1980s - or up until the summer of 1992 when UTV mentions were being factored in again gradually - with visual or spoken reference to anything but "Ulster Television" or the less-frequent "Ulster TV".