I cannot login to my email address

Why can't you log in? Error message(s)?

Reference your name change question, note the restrictions in the article.

Apple ID Name Change.        

 What to do after you change your Apple ID or password - Apple Support    I suggest doing this before you change your Apple ID or password.

Based on what I have read, I suggest you leave your Apple ID email address as a 3rd party email address because you have more flexibility if you need to change the email address. For example, if the Apple ID got compromised, you can change it to another address. I also have read of many people who were locked out of their accounts when they forgot their password. Since the recovery email address is the @iCloud email address, if you forget your password, you also can't access your email to

See what Eric Root said above. It is unclear to me what your circumstances are. But, you also could create a new Apple ID. See 

How to create a new Apple ID https://support.apple.com/en-us/HT204316 See the data implications below.

Some of these things will apply to your situation even if you are not changing your Apple ID: What to do after you change your Apple ID or password https://support.apple.com/en-us/HT204071

 Keep in mind that some things available under a first Apple ID will not be available under a new Apple ID. For example, you won’t be able to transfer anything purchased from the App and iTunes Stores to the new ID. And, there are other issues to be addressed.

See what Eric Root say on this matter here: hthttps://discussions.apple.com/thread/7452747 and

what Winston Churchill says about it here: https://discussions.apple.com/thread/7452747