Long before it meant a scandal, "watergate" was a plain piece of engineering vocabulary.
Etymonline dates the word to the mid-1300s, meaning a channel for water. By the late 1300s it also meant a floodgate, or a gate opening onto a body of water. It was simply water plus gate, and it was used for centuries without any hint of politics.
Nobody is sure where the Washington building got its name. The Watergate complex went up between 1963 and 1971, designed by the Italian architect Luigi Moretti. Wikipedia lists several possible sources. One is the old locks of the nearby Chesapeake and Ohio Canal. Others are the ceremonial "Water Gate" steps near the Lincoln Memorial, and a restaurant called the Water Gate Inn that once stood on the site.
There was a real water gate close by. Greater Greater Washington describes a reinforced wooden dam built in the 1830s at the mouth of Rock Creek. It filled a basin so the Tide Lock could lift canal boats from the Potomac. The article does not claim it as the source of the complex's name, and Etymonline calls the canal link uncertain.
The complex became fashionable, and popular with people in the Nixon administration. The press nicknamed it the "Republican Bastille." On June 17, 1972, burglars were caught inside the Democratic National Committee offices on the sixth floor of its office building. The cover-up that followed ended with Richard Nixon's resignation on August 9, 1974.
The scandal then gave English a suffix. Etymonline dates "-gate," meaning "scandal involving," to 1973, abstracted from Watergate. It has since been bolted onto affairs of every size.
That makes Watergate an unusual case. A building named after a canal structure became the name of a political crisis. The crisis then turned the back half of the word into a tool for naming new scandals.