Your achievements are tied to your gamertag, not the console, so there are a few ways to transfer everything over.
If you have a hard drive on your old console and you're buying one of the older models, you can just pop it over to the new one and your achievements and saved games will be usable right away. If you are buying one of the newer consoles with internal hard drives, you should use a transfer cable to move all the data over to the new console:
If you've purchased a new Xbox 360 console, you can transfer everything (games, videos, music, saved games, gamertags, and even your hard-won achievements) to your new console!
Two options are available for moving your precious information. You can either use the Xbox 360 Hard Drive Transfer Cable to move everything to your new console, or you can connect a USB flash drive if you have only a small amount of content such as your gamertag and saved games.
If you don't have a hard drive, you can either move the data over via the USB memory stick or do a recovery on your gamertag. The recovery will not transfer any hard drive data and will only retrieve your profile. Also, if you do a recovery, be aware that every achievement you unlocked since the last time you connected to Xbox Live will be lost.
From the support page:
You might need to recover an Xbox
LIVE gamertag in the following situations:
- You have a Zune or Games
for Windows — LIVE account and want to join Xbox LIVE.
- You
accidentally deleted your profile, or you want to move your profile to
a new console.
Important
- Any achievements or changes that you have
made since the account last connected to Xbox LIVE will be lost during
the recovery process.
- Do not recover your gamertag to a friend's
console as a convenience. You might lose your saved games. Instead,
follow the steps in Use a gamer profile on another console.
If you have any downloadable content, you might also have to transfer content licenses to your new console.
Once you create an Xbox Live account, your gamertag replaces whatever name you gave the profile. Profile names are local to the system, but Xbox Live account gamertags are unique across all Xboxes, so it's unlikely that he could change it to be "Dave" again - likely someone already has that tag. I do believe you get one "free" gamertag change when you sign up for live (after that it costs points, which cost money), so if there's some gamertag that would suffice for his purposes, he might just be able to change it.
If you have an Xbox Live account and want to buy DLC, it will work fine on all profiles on the first Xbox it is downloaded on, and the profile that purchased the content on any Xbox.
The only downside here would be that if your situation changes, it might not be easy to use content you purchased previously. For instance, if you get your own Xbox and download the previously purchased content to it, it will only work on your profile/account, and not on any others on the new Xbox. There's a "license transfer" option in the dashboard that can get around this, although you'll then deauthorize the content on the first Xbox, and it can be done only once every four months. Needless to say, this gets tricky kind of fast.
For the purposes of free DLC, this caveat likely doesn't matter. You can use the new Silver account your dad created with the "random" gamertag to download free items off the store, and create a new profile with the name you prefer to play with.
Best Answer
No it does not, i created a new live id (chnage of email address) and transferred my gamertag to it (and the points moved as well). I went to close the old windows live account but i could not as xbox live was connected to it. So it does not transfer over as you would think it would.