its not the universe it's called a cluster.
The Universe
For starters, if there were no separation between two (or more) galaxies, it would be considered a single galaxies, not two or more. The reason matter is clumped together into galaxies at all (with separations in between) is because of gravity - gravity tends to do that, i.e., to clump things together.
It highly likely that astronomers will name all the designations of the 100 billion galaxies in the universe in this lifetime.
Astronomers can name all the designations of the 100 billion galaxies in the universe using their mass, age, and metallicity.
Spiral Galaxies
In theory, all galaxies originate from the Big Bang, which is the name that describes the explosion that propelled all matter into the cosmos. All galaxies are moving. All galaxies produce energy like light and gravity. Think of galaxies like you would human beings. Although very different in some ways, they are mostly the same.
That's called a supercluster.
All stars and galaxies are in the universe.
A super massive Black hole present in the centre of almost all galaxies have tedency to bind up all the things . Our milky also have super massive black hole in it's centre .
Galaxies do combine or merge together. In about 4.5 -> 5.5 billion years time time, the Andromeda Galaxy will combine with our galaxy, the Milky Way Galaxy. In a lot of cases Irregular Galaxies are believed to have formed with interactions with other galaxies. See related link for a picture of two galaxies merging.
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.
Some galaxies are bound together gravitationally into what is called Local Groups. Because of the gravitational attraction between them they are approaching each other.