What is the process for adding a dba to a 501(c)3? The DBA is already set up at the county level listing the parent n/f/p as the corporation. What is the process for getting the IRS to recognize it?

If you call it a "501 (c) (3)" you are implying that you already have IRS recognition. This recognition process is not automatic; it can be quite complex actually.

You can supplement your recognition application by supplying the fact that your organization is "doing business as" some named d/b/a. I don't know if this is necessary, however.

As far as anyone I know who was a dba, you just add dba on the title line of your tax return.

I have heard of states that require that business names by run by them because they don't allow certain ones, but you are past that stage?

As far as anyone I know who was a dba...

"d/b/a" is not a noun. It is not a thing. The phrase means, of course, "doing business as", as in "John Smith, doing business as 'Smith's Widgets' ". John Smith might be a sole proprietor, but people who buy widgets from him know is store as "Smith's Widgets". Similarly, if OP's non-profit corporation does business as (some phrase), that doesn't affect who is responsible. Whether the IRS will allow people, who have made charitable donations to the non-profit, to deduct those donations is what 501 (c) (3) recognition is all about. A review of the IRS bulletins and manuals on the subject might answer the question.