You're mixing up several different protocol layers in your question.
If you just enter nothing but "monitor" in the browser URL bar the browser is going to first lookup "monitor" in DNS and finding nothing it will then probably send a query to Google or your configured search engine. In the past browsers have taken other steps, such as appending ".com" and prepending "www." but I don't think modern browsers do that any more.
So far, your server is not even remotely involved.
If you're a large ISP user (TimeWarner, Comcast) and use their DNS it's also possible the ISP will intercept your failed DNS lookup and route the request to a "helpful" search page (i.e. SPAM) of their own.
At this point the request is still nowhere near your server.
I suppose you could mess with the /etc/hosts
file on your local system to resolve "monitor" to the proper hostname, but that's an extremely brittle solution that has to be hard coded on each machine you want to have this "shortcut" link (and which breaks when the hostname changes).
You're much better off just setting up a web shortcut in your browser that points to the right place.