It's possible to create an offline gamer profile on your Xbox 360 that is different from the profile you create on Xbox.com. The offline profile saves achievements earned offline, but doesn't send them to the Xbox servers to be saved with your online profile. It's possible to merge an offline gamer profile with your Xbox.com profile, but it will take some gamertag juggling. Unfortunately, it's not possible to merge two online profiles into a single account; this process is only for gamers who have built up offline achievements before joining Xbox Live.
Open your gamer profile from the Xbox Dashboard or Guide and select "Edit Gamer Profile." We'll use "Player1" as a gamertag.
Select "Profile Name" and enter a new gamer profile name, like "Player 2," then sign out of the Xbox Dashboard.
Select the "Xbox Live" banner in the Xbox Live area of the Dashboard, then select "Join Xbox Live" and follow the onscreen instructions.
Enter your original gamertag ("Player 1," for this process) when prompted. You should get a "Gamertag in use" message. Select the "Recover Gamertag" option and follow the onscreen instructions. You'll be asked to create an Xbox Live membership during this process; be sure to create a free Silver membership, as other membership types cost money. Have your Microsoft Passport Network password and e-mail address available for this step.
Repeat steps 1 and 2 to change the name of your new gamertag to something besides the two gamertags used so far, say "Player3." Sign out of the Dashboard.
Sign back into the Dashboard using your original profile (renamed "Player 2,") then quickly change the profile name back to your original profile name ("Player1.") Your games and achievements will now be associated with your original gamertag.
Repeat step 4 to join Xbox Live using your original gamertag. You'll need to set up another Microsoft Passport Network account during signup, since your original account will stay linked to the "Player3" gamertag. You can delete the "Player3" account from your Xbox, since you probably won't be using it.
You can only change a gamertag on an account if you have Microsoft Points for that account. If you don't have any, you'll have to purchase some first.