My question covers those vessels that are part of a military (either combatant or auxiliary), for either the same or different nations, and with spelling close to each other (so discounting translated names from, say, Chinese to English). If so, did it ever cause significant confusion, especially when a nation was at war?
There is the weird case of the ship that sank itself. When World War I started, the Royal Navy invoked a clause in the construction contract of the Cunard ocean liner RMS Carmania and pressed that ship into service as the armed merchant cruiser HMS Carmania.
HMS Carmania was sent to the West Indies to search for German armed merchant ships. They found the German ship Cap Trafalgar, which had disguised itself as the Cunard ocean liner Carmania. On September 14th 1914, the real Carmania encountered and sank the German ship that was impersonating the Carmania, off the island of Trinidad.
Source: "The Ship that Hunted Itself" by Colin Simpson (1977)
Several of the ships named USS Enterprise overlapped in service ships named HMS Enterprise. As ships are generally identified by type and size, so you probability wouldn't confuse the 12-gun schooner USS Enterprise for the 28-gun frigate HMS Enterprise.