We have Barnard's galaxy NGC 6822.
We have Bode's galaxy, M81.
I think that M83 should be called La Caille's galaxy, not the Southern Pinwheel galaxy because he found it on 23 Feb 1752 with a 0.5" aperture refractor from Cape Town. It is the only galaxy in his list of 42 objects.
La Caille (I 6 in his list) described it as a "small, shapeless (or formless)" nebula. It was one of the first galaxies to be discovered. (After the Milky Way, LMC, SMC, M31, M33 and M32)
William Herschel saw M83 on 15 Mar 1787. He described it as very bright with a bright resolvable nucleus in the middle and faint branches about 5' or 6' long.
On 5 Sep 1826 James Dunlop saw "a very beautiful round nebula, with an exceedingly bright well-defined disk or nucleus, about 7 or 8 arc-seconds diameter, surrounded by a luminous atmosphere or chevelure, about 6' diameter. The nebulous matter is rather a little brighter towards the edge of the planetary disk, but very slightly so. I can see several extremely minute points or stars in the chevelure, but I do not consider them as indications of its being resolvable, although I have no doubt it is composed of stars."
Interesting topic Glen, raises an almost philosophical question. Should objects in the heavens be named after the discoverers or should I say, the first! person to observe them or just be referred to by their catalogue number.
Does create a few problems with the Messier and Caldwell catalogues or others though. If "we" are calling catalogues after the compilers of said catalogues then giving individual objects common names is no different.
But, dare I say that the object in question has been known as M83 for a few centuries now and most of us, on hearing the moniker, know precisely what object is being referred to.
Personally I like the proposal but it would be a long process to get another moniker to be accepted.
Thanks Jeff for your comment
I like the Messier catalogue because he collected all the known DSO at the time.
I am not keen on Caldwell and others naming objects after themselves, if they did not find them.
W & J Herschel found hundreds of objects. we can't name all those objects after them.
Caroline Herschel only found one galaxy. I think NGC 253 should be called Caroline's galaxy. It is a better name than the Silver Dollar.