Static modifiers cannot appear on a type member (TypeScript error TS1070). That's why I recommend to use an abstract class to solve the mission:
Example
// Interface definition
abstract class MyInterface {
static MyName: string;
abstract getText(): string;
}
// Interface implementation
class MyClass extends MyInterface {
static MyName = 'TestName';
getText(): string {
return `This is my name static name "${MyClass.MyName}".`;
}
}
// Test run
const test: MyInterface = new MyClass();
console.log(test.getText());