Help: Apple ID - Alias Email

I think you mean that you started with an @mac.com email in the days of DotMac - is this correct? The DotMac email address would have been the ID as well. When DotMac closed and was superceded by MobileMe you aquired an @me.com address with the same text before the '@'. Later, when that closed and iCloud opened, you also acquired an @icloud.com address with the same text before the @.

These three addresses are effectively the same thing, and you can't separate them: just don't use the ones you don't want. You can continue to use and log in with the @mac.com version (I do the same thing) though you can also log in with the other two.

So, your ID is a Yahoo address which you use to log into an iCloud account where you have a primary email of something@me.com and something@icloud.com, the 'something' being the same. Changing the password on the ID changes it on anything you use it to log into.

You can change the Apple ID to the iCloud address, or to another non-Apple address. I guess that what you want to do is to make the Apple ID the iCloud address, and have the Yahoo address not acting as a sign in - is this correct? Here is the procedure:

1. Firstly, sign out of iCloud on all your devices: go to each of your devices and sign out in System Preferences (or Settings)>iCloud - 'Sign out' on a Mac, 'Delete this account' on an iOS device (this will not delete the account from the server). If you have 'Find My iPhone' etc enabled you will need to disable it first. Your synced data will disappear from your devices but will reappear when you sign back in.
2. Create a new email address, for example at Yahoo or Gmail, or anywhere convenient (or you can use an existing address as long as it is not associated with an Apple ID). You can change it to another Apple address only if it's listed when you click the link to change (in practice this means your main @icloud.com address, and the equivalent @me.com and @mac.com versions if you have them: it does not include email aliases).
3. Go to http://appleid.apple.com and click 'Manage your Apple ID'. Sign in with the current ID.
4. Where it says 'Apple ID' and gives your current ID email address, click 'Change your Apple ID'.
5. Enter your new address and click 'Save changes'
6. Sign back into iCloud on all your devices with the new ID and password. Your synced data will reappear (give it time).

I reiterate - before you start, sign out of iCloud on all your devices. Failure to do this will lead you into difficulties.