I wouldn't recommend it. Generally ASUS is happy to let people use the logo in derivative artwork but you're talking about using it as an identifying mark. There's a possibility people could confuse you as being an official ASUS stream which ASUS would not want. As a small streamer it's unlikely anyone would bother but if you ever blew up ASUS would probably make you change it. Better to come up with a logo now that is uniquely you that you'll be able to keep as you grow your channel.

Note that I'm not an ASUS employee and I'm not a lawyer. I'm just giving you advice based on what I've seen as typical protection of business marks.