The short answer is: No, there doesn't seem to be any nickname in use;
it's just referred to as "IC 1101" (which is pretty easy to write and
say; I'd argue it's better than "UGC 09752" or "PGC 054167", which are
among the 52 other names listed for it by the NASA Extragalactic Database). It's also sometimes referred to as "Abell 2029-BCG", which means it's the brightest galaxy in the galaxy cluster Abell 2029. Not very exciting, but that's how it is.
Perhaps a more interesting question is: Should it have a special nickname?
Put another way, is IC 1101 actually the biggest galaxy in the known universe?
Part of the problem is that galaxies don't have well-defined edges, so it's ambiguous how one should properly define their "sizes". In fact, so-called "dwarf" galaxies are usually defined in terms of their luminosity (absolute stellar brightness), or sometimes in terms of their total stellar mass. This means that a diffuse, faint, low-mass galaxy might be labeled a "dwarf", even though in some respects it has a larger size than a more compact but brighter and more massive galaxy.
Kluge et al. (2020) is a recent systematic analysis of deep images of the central galaxies in 170 relatively nearby clusters in the northern sky -- one of which is IC 1101. Among the measurements they made was the "half-light radius" -- basically, the radius estimated to contain about half of the galaxy's total stellar light, and a very common way of defining galaxy "sizes". The useful thing in this case is that all the galaxies are measured in the same way, using the same kind of data, so you can make comparisons a bit more robustly than "well, in this paper IC 1101 has this size, but in this other paper -- which defined the size differently and used a different kind of data -- another galaxy has a larger size ...".
Table 4 in Kluge et al. lists two different half-light-radius measurements for each galaxy, which for IC 1101 gives us either 261 kpc ["kpc" = kiloparsec, or about 3000 light years] or 329 kpc. (For comparison, the half-light radius of the Milky Way is probably about 4 or 5 kpc.) Using the first value, there are about fifteen galaxies larger than IC 1101; using the second value, there are about twelve. If we go by their absolute magnitudes (total stellar brightness) -- a very inexact proxy for how many stars they have -- then it's much more prominent; but there are still two other galaxies that are brighter.
So IC 1101 probably isn't the "biggest", even if you can find excitable web pages which say so.