The filing is all that is required. I do not see why you would obtain a second EIN if the LLC is a trade name for the original one. You can make it a subsidiary and keep is as a single tax entity and there is far less tax filing to do. There should be only one annual registration fee required unless the state determines that these are two distinct businesses and should be legally separate.
The questioner might find some of my legal guides helpful:
From my legal guides on law in general and about attorneys
Is it Legal? Is it Illegal?
Selecting and Hiring a Lawyer
Understanding the Different Court Systems
An Introduction to Legal Terms used in Litigation
How to Succeed in Business.
Taxes Rules and Regulations
Mr. Sarno is licensed to practice law in NJ and NY. His response here is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply inappropriate. Mr. Sarno strongly recommends the poster confer with a NJ business attorney.