Showing different site title based on parameter passed in URL

[miner2049er]

For the test site:

www.simobile.com/wordpress

in the Dashboard, in Settings -> General -> Site Title is currently "Fred Fish Real Estate."

Which gets shown in the header *AND* the URL of every page.

If for testing with a client, different business name wordings, such as "Fred Fish Homes" or "Fred Fish Realty" in the text of every page header/URL, how would I pass a string from a URL like:

http://www.simobile.com/wordpress/?t...0Fish%Realtors

to the initial browser open, so that the GET parameter I passed persisted once the client starts to click around and away from the initial home page?

I DON'T want this stored in the WP MySQL database, as I may have two different clients (with different names) accessing the same codebase, so I guess I am looking at a cookie/sessions based solution? Especially, as the client may come back later and click on a bookmarked link, and not one in an email.

I guess I am hosed though, if the client decides to share the link with someone else but without the URL parameter coming along for the ride.

Hope I've described what I'm after clearly. In what places would I modify WP?