There are persistent grumblings about the length, tongue-twisting, and Unity/Unification-like nature of the term Unitarian-Universalist. Right after the two denominations consolidated there was a strong push to change the name to the Liberal Church or Liberal Christians, but the proponents were outmaneuvered and the name Unitarian-Universalist hasn’t been challenged on the institutional level since.
It’s worth recalling that neither Unitarian or Universalist (to say nothing of Unitarian-Universalist) were predestined names. During the formative period of Universalism some people actually preferred the term “Universalian” to that of “Universalist.” So modern day UUs could’ve ended up calling themselves Unitarian-Universalians, for example. Or perhaps Unitarian and Universalist could’ve been retired in favor of Universalian as the name of the new denomination back in the 1960s. Universalian: it sounds a bit unusual, but perhaps it implies not just universalism of theology and fellowship, but also a sort of universe-oriented thinking, outward-looking toward the cosmos and consistent with a modern, post-geocentric approach to life and meaning.
There were terms for the Universalists’ opponents that have also fallen out of favor at this point. Universalists used to refer to other Christians as Partialists or Limitarians, because they had a partial or limited view of salvation vs. the Universalist/Universalian understanding of unlimited salvation and total reconciliation of man to man, God to man, and man to God (as the language of the day would put it).