The Fellowship of the Ring question

Some are his own invention, especially the Elvish, but even these are sometimes influenced by his knowledge of other languages. He was fluent in Anglo-Saxon, which is where he gets some of the names of the people of Rohan: Eomer is a name that appears in "Beowulf" and means "horse-famous". Other words and names show the influence of Celtic languages. For example, "dun" in Tolkien's "Dunadan" means "Man"; the Welsh word for "man" is "dyn" (pronounced "duhn"). Many of the names of Tolkien's dwarves come from sources such as the Elder Edda and other ancient Nordic histories and legends. "Gandalf" is Old Nordic for "Wand-Elf," and appears in a 13th-century Scandinavian text.

He invented them.

Very true, he created whole languages for the various races of Middle Earth. Most of the names, perhaps all, are translated from the tongue that he created. As an example Galadriel's name was given to her by Celeborn. Galad in the Sindarin tongue meant light and riel meant garland maiden. Hence, garland maiden of light. As you remember, she is often referred to as the "lady of light." This is just one of many examples. For anyone interested in Tolkien, The History of Middle Earth books go into great detail about his many writings.

Tolkien was a linguistic.Most of the creatures and names in the novel are from Scandinavy. He also also used Runic alphabet-the ancient alphabet of Scandinavy.

I'm not 100% certain, but like 99% that somewhere I read that as a linguist, Tolkien first made up all the languages, old and new, of Middle Earth, and then came up with a universe to put them in. That being said, a lot of the names, especially Elvish, as said above, are simply descriptions of the people or places in other languages.
Other names, particularly the dwarves' names from The Hobbit, do come from Norse mythology (where much of Tolkien's inspiration came from).
Many of Tolkien's languages also mirror languages Tolkien himself studied.

I wish I had his talent for naming ! I have no imagination in naming things - pets etc.
Parr of my enjoyment of the series is seeing what wonderful names he gives places - Mordor, Mist Mts. Rivendell - all resonate somehow.

Tolkien was a professor of language and published a treatise on Beowulf that is considered the definitive academic work on the subject. He made them up based on his knowledge of language and myth to fit the setting.

If you read the appendices, Tolkien is pretending that LOTR is a translation of an actual story, and that "Samwise Gamgee" is a translation of the feel of the actual name Banazîr Galbasi." Banazir means "halfwise" or "simple" so Samwise is the stolid, faithful friend originally from the village of Galbasi.

So basically Tolkien made them up based on his expertise. Not all academics are stuffy. Tolkien was pretty damn cool.