The Royal Navy has had several such significant recurring names.

Ark Royal is one of the most frequent in the 20th Century. The first Ark Royal was the flagship of Admiral Howard during the Spanish Armada campaign in 1588. As such, she took part in the battles in the Channel, and the battle of Gravelines. She would also take part in several later campaigns against the Spanish, but would be sunk accidentally in 1636. In 1914, the name was given to a comparatively unimpressive seaplane carrier, converted from a merchant ship only just under construction. This new Ark Royal was the first ship built specifically to carry and launch aircraft, and had the further distinction of being the only aircraft carrier to have a sail (she had one on her mizzen mast, to keep her head to wind for aircraft operations). She served with distinction in the Mediterranean during WWI, providing air support during the Dardanelles Campaign. In the post-war period, she transported aircraft around the Empire, before a catapult was added to test designs and techniques. In 1934, she was renamed to Pegasus to free up the name for a carrier being built. The 1934 design Ark Royal was a large, modern aircraft carrier, completed in 1938. She served in several theatres of WWII, taking part in the Battle of the Atlantic, the Norwegian Campaign and the Mediterranean Campaign. Her battles included the attack on the French Fleet at Mers El Kebir and the Battle of Cape Spartivento, though her most famous action was crippling the battleship Bismarck in 1941. On November 10 1941, she was struck by a single torpedo from U-81, which blew a large hole in her hull and knocked out her electrical power. This hampered initial attempts at damage control, though this was quickly abandoned, as the crew evacuated. She could probably have survived the torpedo hit, but her captain abandoned ship early to ensure that her well-trained crew survived. The next Ark Royal was an Audacious class carrier laid down in 1943, but not launched until 1950 or completed until 1955 thanks to cuts in naval spending following the end of WW2. She had a long career, serving until 1979. During this, she received several upgrades and refits, allowing her to keep operating the heavier aircraft of the post-war period. Following her decommissioning, the last Ark Royal was an Invincible-class carrier, launched in 1981. She served until 2011, taking part in the second Gulf War.

Another such name is Dreadnought. Dreadnought tends to be reserved for transformative ships, at least in recent years - the most well known is probably the 1906 Dreadnought, which transformed the modern concept of the battleship. However, its predecessor, launched in 1875, had a similar effect on creating the concept of the battleship that its successor would replace. The latest Dreadnought was the Royal Navy's first nuclear submarine, and the next will be the first in a class of SSBNs.

There are a limited number of navies in the world that still exist as a force and have the historical backgrounds and traditions on the scale of the US Navy.

Other than the Royal Navy, all of the nations with a significant modern navy have undergone at least one, usually several, instances of complete political upheaval that has tended to break up ship naming conventions in favor of more politically acceptable alternatives to the new regime in each case. (French, Russian, German, Japanese, Italian navies, etc..)

The Royal Navy has a large number of traditional ship names that have been used many times over. There have been 8 ships named HMS Royal Sovereign, 8 named HMS Renown, 9 named HMS Dreadnought, 13 named HMS Revenge, etc…

As for the US Navy and USS Enterprise, the name has been used 6 or 8 times, depending on which ships are included in the list, but it wasn’t really until recently that it became a given that there would always be a major ship named Enterprise. That started in World War II with the performance of USS Enterprise (CV-6) which earned 20 battle stars in the Pacific theater. The first nuclear-powered carrier (CVN-65) was named after CV-6 due to the history of that carrier, and the newest (CVN-80) is named after the two previous carriers.

There are other US Navy ship names that have been used as often, or even more often than Enterprise. There have been at least 6 named USS New York, 8 or 10 named USS Massachusetts, and 10 named USS Virginia, for example.

USS Enterprise is unique in the sense of public visibility brought on due to the popularity of Star Trek, which directly led to the first (test) space shuttle being named Enterprise, but most people aren’t really aware of the reason for the new ship’s name in terms of the history of CV-6 and CVN-65.

I'll spare you my own personal ranting about the naming of US Navy ships in recent years.

EDIT: formatting.

In Peru we have El Huascar. It was the ship used by Admiral Miguel Grau, a national hero and militar martyr, during the Pacific War with Chile (1879-1883) Grau died on the Angamos battle after fiersely fighting off the chilean ships for more than five months. Its was because of his defeat that they could finally invade Peru by land. El Huascar was captured and is till this day in Chile.

Its called El Huascar in honor of the Inca Huascar, son of Huayna Capac and brother of Atahualpa.

Source: web.archive.org/web/http://www.ccffaa.mil.pe/cultura_heroes_Grau.htm