In New York City there is a practice of assigning more prestigious sounding addresses to large buildings. Most of these addresses use the word "plaza." This practice was prevalent in the second half of the twentieth century. I have heard that the practice was stopped at some point, with existing buildings keeping their designations but no new designations being allowed, but I don't have a good reference for that.
From a New York Times article on the topic from December 30, 1973:
The post office has a growing headache that might be termed the plaza syndrome.
To its dismay and that of city officials, an increasing number of owners are bestowing upon their new office buildings fanciful addresses apparently chosen to create the kind of prestige that might attract tenants.
The article then mentions 1 Liberty Plaza (actual address 91 Liberty Street) and says
Since 1960, the Manhattan Borough President's office and the City Council have authorized plaza designations for 24 major structures. The United States Postal Service has accepted those official plaza names, but insists that they be used in conjunction with conventional street addresses, including ZIP codes.
Many major tenants in the 24 “official” plaza buildings ignore that regulation. Moreover, there has been what the borough president's office calls “a proliferation of illegal plazas” as 20 or so buildings close to those with “official” designations adopted the plaza names as part of their addresses.
Some buildings, of course, have such prominence that they transcend an address—the Pan Am Building, for example, the Empire State Building or the World Trade Center. But officials say that many new structures lack such prominence and have adopted plaza addresses, authorized or not, that are inexact and even misleading.
The building known as 1 State Street Plaza, for instance, cannot be entered from State Street. Its lobby is at 44 Whitehall Street. And the structure next door, just to the north of 1 State Street Plaza, is 1 Battery Park Plaza. Its entrance is at 1 Pearl Street.
Somewhat later, discussing 1 New York Plaza:
To make matters worse, two nearby buildings have, without city or post office authorization, adopted New York Plaza addresses. They are 4 New York Plaza, with a main entrance on Water Street, and 2 New York Plaza, which has a lobby facing South Street.
The article then mentions a building that has unofficially called itself 2 Dag Hammarskjold Plaza despite being downtown from 1 Dag Hammarskjold Plaza, "which ignores the convention that higher numbers are to the north."
Notice how the article overlooks the fact the the World Trade Center isn't a single building but instead comprises several buildings. As others have noted, these buildings have similarly been identified by number. Since "center" is already a noun indicating a place, even though it is not a traditional street designation, there was apparently no need seen for an additional noun such as "plaza."
Since the twin towers were designated one and two, it is natural for the single tower that replaced them to be designated one. While addresses are normally written with digits, it is not unheard of to use words. Thus, One World Trade Center.