Was this a particular channel/app? I've never seen a Roku say, "Welcome back" and you don't sign into a Roku account on a Roku device. Each channel/app may have a sign in, but not each device.
I was about to post the same thing. You probably just need to log out of your account on that particular channel. Look for an "Account (often just an icon shaped like a head)", "Options", "Settings", or similar link to click, then look for some way to "Log out", "Disconnect" or something similar.
Roku Streaming Stick +, 3810X, Ser YH0059427035, wifi - Samsung UN55ES6100
Roku Streaming Stick, 3600X, Ser 5S56D8240827, wifi - JVC EM37T