Are these the same businesses using 2 names, or 2 different businesses using 2 names? It's not a good idea for 2 businesses to share the use of a business name, since the liabilities of one will affect the profits of the other (and vice versa), and it also can be an accounting and trademark nightmare for two different businesses to operate under the same corporation.
Your query is unclear about you're trying to do, try rephrasing, or seeing a corporate lawyer who you can explain everything to.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
I agree with my colleague that the intent of your question is not clear.
I suspect you *might* be asking whether a fictitious business name (DBA) that you have been using as a sole proprietor can be assigned to your corporation (presumably because you no longer need to use it as a sole proprietor).
If that is the case, you should find the post at the link below helpful.
Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.
I agree with Mr. Schultz, and think you will find is blog post helpful. I would add, that your corp or business entity can have multiple DBA's of FBN's but you really ought to consider your purpose, because others have stated you could be creating an accounting and nightmare. Likewise, you are likely to experience problems if you or the corp gets into problem with a liability. If you do business using the corp name, but treat the activity as a sole prop activity, the corp can be liable. Further, if the corp sustains a liability using the sole prop name you could be liable and the limited liability protections of doing business as a corp could be out the window. There are volumes of information on piercing the corporate veil, reverse peircing, and the "alter ego" analysis. If you are not going to have an attorney assist you, you should at a minimum review these principles.
Best of luck!
This answer is provided for academic purposes and the asker is encouraged to speak directly with an attorney on their matter.