Remaining anonymous on a wireless network doesn't mean the operators won't detect your existence in the network. It's essential to understand the core concept of what is going on here: you're asking the access point (AP) to give you data, the AP will give you said data, it will be possible to detect that someone is using the connection.
To remain anonymous you should either constantly change your MAC address; IP address; and clear your cookies (Captive Portal software can identify you using a cookie in your browser), or you can impersonate a legitimate client by using their MAC address; IP address (in case it was assigned statically); and the identifying cookie in the browser.
Please note that it's not common for the regular access points to have Captive Portal software, especially in a home or small office environment. So it's relatively safe to ignore the cookie part.