Why is Waterdeep known as the City of Splendors?
Ed Greenwood thought it was a catchy nickname.
Waterdeep, also known as the City of Splendors or the Crown of the North, was the most important and influential city in the North and perhaps in all Faerûn.
The city was the hub of trading from the mineral-rich lands to the north, the merchant kingdoms of Amn and Calimshan to the south, the kingdoms of the Inner Sea to the east, and the sea kingdoms and traders to the west. Waterdeep's authority extended between thirty to forty miles from its walls.
Waterdeep was named for its outstanding natural deep-water harbor, and the city that grew up at this site became the commercial crossroads of the northern Realms. More than 100,000 people made their home in Waterdeep
Beyond that, it was the appellation chosen for the 2e campaign setting material published for the forgotten realms. Ed Greenwood is the original creator of the Forgotten Realms setting, and thus he can call it whatever he likes.
My copy of the 1987 Forgotten Realms Cyclopedia names Waterdeep as "the City of Splendors." It's the largest population center, a mercantile capital, and at 100,000 holds more people than all of the cities of Cormyr. (p. 87, Cyclopedia, Forgotten Realms, TSR, 1987, AD&D 1e).
As to cities branding themselves to attract attention or to brag on themselves, see Chicago being called "the City of Big Shoulders" and "The Windy City," New York City being called "The Big Apple1" or "Capital of the World" and Paris calling itself "City of Light." Also worth noting that Imperial Rome referred to itself, as caput mundi, meaning "Capital of the World." (Thanks @KRyan). To this day it is often called "the eternal city." (Thanks @Rad80).
1 As @KRyan helpfully points out ... New York City has also been named with other aliases, to include The City That Never Sleeps, Empire City, and Gotham among other things. Given that New York (the state) is called "The Empire State" ...