How do I change my Activision ID

You would have to go through their support

Microsoft does not own activision at this time and if/when that goes through, they will likely still maintain their own teams

https://support.activision.com

Change the WLID associated with my gamertag.

If for any reason you want to change the WLID you have associated with your account, all you need to do is follow these simple steps.

1. On the console, go to My Xbox, and select your avatar.
2. In Account Management, select “Manage Account”.
3. In Your Information, select “Windows Live ID”.
4. Select “Change Windows Live ID”.
   1. If you have another Windows Live ID, select “Yes”.
   2. If you do not have another Windows Live ID, on a computer, go to Welcome to Windows Live ID, and click “Sign up”.
      
5. Enter the password for the Windows Live ID that is currently associated with your gamertag, and then select “Sign in”.
   
6. Enter the email address and the password for the new Windows Live ID that you want to associate with your gamertag, and then select “Sign in”.
   
7. Select “Yes, change” to change the Windows Live ID associated with your Xbox LIVE account.
   
8. Select “Update Contact Information” to update your contact information, or select “Done” to finish
   

How do i change my windows live id?

modern warfare gave you the choice to use the one they give you or make your own new activision ID . you must have not read the instructions and terms before accepting. im unsure if it can be changed but if it can be changed anywhere it will be via activision.

i have just read though that it can be changed and this is what i found -> To change your display name in Modern
Warfare, you need to go to the Activision website. Once there, login to your Activision account or create one if you don't have one already. After you've logged in, go to your Profile and then
select Basic Info. You should see Activision ID at the bottom.

I changed my gamertag and its half done it. What I mean by that is on games like GTA Online, Black Ops 4 and Fortnite its registered the name change. On Modern Warefare it hasn't registered the gamertag change and it still displays my old gamertag on a Xbox
party and on my sons friends list.

Anyone else had this issue?

The reason CoD:MW doesn't display your new gamertag is likely the following:

In order to allow MW to be cross-platform, Activision requires players to login to an Activision account when installing the game. This account contains an ID that is then used by Activision to connect players to the MW server regardless of gaming platform.
When in game, press start to access the options and then tab over all the way to the right and then select Activision account. You will see your Activision ID as well as a display name. You should be able to edit the display name from there to make it reflect
your new Xbox gamertag.