Q: How can I change my icloud ID?

I assume you changed your Apple ID following this procedure:

Sign in with a different Apple ID on your iPhone, iPad, or iPod touch - Apple Support

If so, see the paragraph:

If you're no longer using the email address associated with your Apple ID, you can change the email address that you use as your Apple ID, then use the steps below to update it in the services on your device. If you forgot your Apple ID, there are a few ways to find it.

and the above link takes you here:

Change your Apple ID - Apple Support

Is your Apple ID not also your iCloud ID? They are typically the same. You can't change your iCloud email address, but you can create an alias for it that functions exactly the same.

iCloud: Create or change email aliases