Apple id change and 2-factor authentication

No, in fact, the odds are very good that you can't.

See Two-factor authentication for Apple ID https://support.apple.com/en-us/HT204915 and more specifically the section entitled Can I turn off two-factor authentication after I’ve turned it on? This section says: 

"If you recently updated your account, you can unenroll within two weeks of enrollment. Just open your enrollment confirmation email and click the link to return to your previous security settings. Keep in mind, this makes your account less secure and means that you can't use features that require higher security."

This quote emphasizes the security-related importance of two-factor authentication. I would not turn it off even if you are able to. Another reason for not turning it off is that if you use two-factor authentication, then you no longer will have a need for security questions. They are turned off when two-factor authentication is activated.

2 Factor Authentication is tied to your Apple ID, not to the phone.

From the article below updated on 24 Apr 2020. If it has been on longer than 2 weeks, you can't turn it off. 

Can I turn off two-factor authentication after I’ve turned it on?

If you already use two-factor authentication, you can no longer turn it off. Certain features in the latest versions of iOS and macOS require this extra level of security, which is designed to protect your information. If you recently updated your account, however, you can unenroll for a period of two weeks. Just open your enrollment confirmation email and click the link to return to your previous security settings. Keep in mind, this makes your account less secure and means that you can't use features that require a higher level of security.

Apple ID -Two-factor authentication.