The SAP Center in San Jose, CA is sometimes called the “Shark Tank” because the San Jose Sharks play there. The Chase Center in Oakland, CA is sometimes called “Ballhalla” because the Golden State Valkyries play there. What are some more examples?
The United Center in Chicago (home to the Bulls (NBA) and Blackhawks (NHL)) is sometimes unofficially called “The House That Jordan Built,” a reference to a specific player: Bulls star Michael Jordan. The arena was constructed during the Bulls’ first Jordan-led “threepeat” championship run in 1991-1993, and their second threepeat (1996-1998) occurred shortly after the Bulls began play in the building.
I guess there’s not enough of these to warrant a Wikipedia category. I did manage to find the PHX Arena, known as “the Snake Pit” when it was home to the Arizona Rattlers.
Not many anymore, especially not outdoor venues. In the 1960s through 1990s, multi-purpose stadiums were common, and were homes to both NFL and MLB teams, but those stadiums were nearly always sub-standard for at least one of those sports, and they’re now pretty much extinct.
However, indoor arenas very commonly are home to both basketball and hockey teams. Most U.S. cities which have teams in both the NBA and NHL have one venue where both teams play.
I meant multi-use venues which have well-known nicknames. 
Do people still call the Honda Center in Anaheim the”Duck Pond”?
Sometimes it’s even an official name. The football field in Cleveland was, for some years, officially just called “Browns Stadium”.
San Francisco, actually.
Whoops, you’re right. Thanks for pointing that out.
Also Giants Stadium (shared with the Jets) and Yankee Stadium (shared with the football Giants.)
I was going to suggest “the Black Hole,” for Oakland-Alameda County Coliseum, the former home of the Raiders and the A’s, a nickname which expressly refers to the Raiders’ fans, and the black in their uniform.
However, it appears that the nickname refers to a specific section in the stadium during Raiders games, where fans were known to dress in elaborate black-and-silver costumes, and for their raucous and intimidating behavior, as well as being a nickname for the fans themselves (alongside “Raider Nation”).