To a point, the IRS could care less what you name your business or what name is used in "DBA". When you apply for an EIN, you are required to associate that EIN with an SSN. When using the EIN, only two entities know what SSN the EIN is tied to; the business owner(s) and the IRS. Those are the only two entities that "need" to know that too.
What does matter after getting an EIN, is if you later change the name of your business, or if you change the structure of your business. For example, if you change from an LLC to an S-Corp, there are procedures that must be followed and you "may" be required to obtain a new EIN for the new structure.
