There is no direct connection, however, there is a very indirect relationship.
Gimli (Heaven) the town was settled by immigrants from Iceland and named in 1875, long before the writting of Lord of the Rings (1937 to 1949). Iceland's language has its roots in Scandinavia. The boy's name Gimli is of Old Norse origin and means "Fire"
JRR Tolkien was a linguist and was fascinated by the Scandinavian languages and read many of the ancient stories in their original languages. Many of the names used by Tolkien for his characters have some basis in these Scandinavian legends.
The relationship would be that both the character and the village got the inspiration for their names from the roots of the Scandinavian language.
greedy
Gimli son of Glóin is a character in Tolkien's LotR. He is a Dwarf fom the Lonely Mountain, the son of Glóin who also appeared in The Hobbit. Gimli is a member of the Fellowship of the Ring.
frodo bagins the hobbit FAMILY FEUD: frodo gandalf gollum legolas aragorn sam gimli
Moria All Dwarven realms are underground but the one I think you are referring to are the Mines of Moria, Khazad-dum. It was destroyed and abandoned when the Dwarves woke up the Balrog. Other popular Dwarven realms are in Erebor, Iron Hills, Blue Mountains (and after the War of the Ring, the Glittering caves where Gimli was the lord).
See related link for one of the largest Lord of the Rings fan clubs on the net.
Gimli
greedy
He represents the dwarves in the fellowship.
Gimli can be a playable hero on the map Mines of Moria
The correct spelling is Gimli.
Gimli son of Gloin, a brave and sturdy dwarf.
Most people have there own opinion but my favorite is Gimli and Legolas
They were the preferred weapon of the dwarves. Gimli carried an axe.
TolkienTown.com. Tolkien Town has many collectibles and replicas.
Gimli is a dwarf warrior in Middle Earth during the Great Years. He was a member of the Fellowship of the Rings. The character is from the trilogy "Lord of the Rings" by J.R.R. Tolkien.
Gimli son of Gloin, a brave and sturdy dwarf.
Their horse, Arod, is white (grey).