Milky Way, M31 (the Andromeda Galaxy), the Triangulum Galaxy, the Large Magellanic Cloud, the Small Magellanic Cloud, ...
M87 is one of the most prominent galaxies followed by the elliptical galaxy Messier 49.
Andromeda, Milky Way These are galaxies ^ Orion Nebula Eagle Nebula
The collection of all visible or detectable galaxies is known as the universe. Each galaxy is a vast collection of stars--billions of them. Some galaxies have trillions of stars.
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.
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.
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To the best knowledge, there are an infinite number of galaxies, which means they don't have names!
There are about a 100 known blue shifted galaxies. The most well known, is the Andromeda Galaxy.
Some galaxies would be older than others; the oldest galaxies formed pretty soon after the Big Bang - the oldest known galaxy formed about 750 million years after the Big Bang.
Elliptical, Irregular, and Spiral
Yes. See related question.
Some names I've heard are: The observeable universe The local universe