Generally speaking, if all you have done is changed your business name, there is no need for a new EIN. You would note the name change on the your tax return when you file. I agree with the previous responders who recommended that you seek legal counsel on this issue as there may be additional facts that should be considered.
You should not require a new EIN, and your prior name should be registered as a dba.
You are clearly in need of a bit of business and accounting counsel.
To the PROSPECTIVE client, please call myself or another attorney for your choice with more detaiils and an appointment. My PRELIMINARY answer to your question(s) is for general purposes and based upon what little information you have conveyed. It is based on such limited information that the general answer should never be relied as a reason for your action or inaction. My response does NOT establish an attorney-client relationship and such may only be established by mutual agreement, and the signing of a written retainer agreement, which will generally require payment for our services, as this is what we do for a living and, just like you, we must get paid for our work.. .
I hate to answer your question without answering your question but a lot depends on other facts that were not disclosed in the question. I too suggest that you contact a business attorney to be able to fully counsel you on this situation.
Every case is different. As such, the answer cannot be considered legal advice nor can it constitute an attorney-client relationship.
See attached link to IRS publication 1635 which will answer your particular question.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.