I would be absolutely surprised if it wasn't called Olympia Arena/Place/Center/Stadium..
"The arena itself would cost $450 million. Olympia would contribute $11.5 million annually for 30 years toward the construction debt for the 650,000-square-foot arena. The DDA would contribute $2 million a year. And another $12.8 to $15 million a year would come from property taxes paid within the city's downtown development district.
Olympia would also invest $200 million in developing the proposed entertainment district, bringing the development's total price tag to about $650 million." - Mlive