To the best knowledge, there are an infinite number of galaxies, which means they don't have names!
Elliptical, Irregular, and Spiral
M87 is one of the most prominent galaxies followed by the elliptical galaxy Messier 49.
There aren't really any other names for a galaxy that I can think of, but there are galaxy classifications, such as spiral galaxies (that can rotate either clockwise or counter-clockwise), elliptical galaxies, and irregular galaxies.
Canis Major Dwarf and Small Magellanic Cloud are irregular satellite galaxies of the Milky Way.The two irregular galaxies that orbit the Milky Way are the Large and Small Magellanic Clouds.
The Black Eye galaxy. Bode's galaxy.
It means it's the numbering from the Atlas of Peculiar Galaxies, by Halton Arp.
There are approximately 100,000,000,000 galaxies in the visible Universe. To name them all, at one a second would take about 3,169 years. So I won't bother. See related question for some of them.
Andromeda, Milky Way These are galaxies ^ Orion Nebula Eagle Nebula
We know the names of lots of galaxies--that is, the names we give them. I'm sure you're most familiar with the Milky Way Galaxy. You are here. Other well-known galaxies include the Andromeda Galaxy, which is our next-galaxy neighbor, and the Sombrero Galaxy, which resembles a sombrero.
Milky Way Galaxy (ours)Andromeda galaxy.Pinwheel GalaxySunflower GalaxyWhirlpool GalaxyTriangulum Galaxy
Some names I've heard are: The observeable universe The local universe