How do I keep my Adobe stock portfolio if I have to migrate to another account.

Your request is very confusing, as you don't tell us, if you had an individual subscription (paid by the employer) before the change. If that is the case, you just need to attach the account to a different private e-mail address, and you are done.  https://helpx.adobe.com/manage-account/using/change-email-address.html

You still need to be careful, if your businass credit card is attached to that account, as any subscription you would take on that will get that card charged. If you take no subscription, you are fine.

Your e-mail is your Adobe ID, so only if your e-mail changes, your Adobe ID changes. It is always a bad idea to use the work mail address for private stuff for all different reasons, but the most obvious is, that you may lose access to that e-mail at any time, as the employer controls that.

If you are part of a Teams or Enterprise account, you will have two levels. One level is the private level, the other is the buisness level. If I'm correct, you can't use a buisnes level login to create a contributor account. 

When going to https://account.adobe.com and you select your personal account when asked the sign-in, you may be able to change the attached e-mail. Then you would be fine. The contributor account will follow.

I once changed my contributor account password, which is your Adobe email, then it becomes a new one, and the login account is also new, change it in the image in the upper right corner.

You say: "they want us to use a different account and cancel the one we were using". Who is the "we" you're referring to? Adobe Stock accounts, unless they belong to an approved agency, are for sole providers. Per the Adobe Stock Contributor Agreement, each Contributor must certify that they alone own the copyright and all legal rights to the assets they upload. 

I don't believe it's possible to migrate stock images to another account.  Why do they want you to create a new one?