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Sure, no problem. If the company pays for it, use a company provided e-mail. If you are paying for it, use a private e-mail as the Adobe ID.

Be sure that you understand the terms of your subscription, especially the cancellation terms.

Do you mean:

1. Are you allowed to? - Yes, but the license is tied to your email address.
   Can be inconvenient if you're using a company email address in a company trying to control their software licenses. When you leave and your company email address is deactivated, the company loses access to the login.
2. How to? - See reply from @Manan Joshi if it's your personal Cloud plan which you want to access via a company device.