"VIP Sports Center", "Business Sports Center", "VIP Sports Center". Or single column expressions such as: "Royal Tennis Court", "XXX Hotel Basketball Court", etc.!
If there are different places for employees and guests, you can call it a "guest sports center", etc.!
The multi-functional one is called "XX Hotel Sports and Leisure Center"! Or call it "XXX Hotel Supreme Member Sports Center" (anyway, you will be charged for using it, or it can be a membership system, so the hotel can charge a membership fee in advance)! .