I've re-written in a summarized flowchart form what I've
previously mentioned (since that seems to be too much for many of us to digest) on whether or not you need to reveal your former name when applying for jobs (if asked; if not don't mention anything unless they want to check a record that's under that name, and if they ask only if specific information is under another name answer appropriately), applicable to the U.S. only.
1. Is this a "high security" job (such as one with the government and/or requires a security clearance, law enforcement, etc.) where they'll do an investigation that in general legally can't be done by an employer? If yes, go to Step 7. If no, go to Step 2.
2. Do you have
any criminal history on record under your former name? If yes, go to Step 7. If no, go to Step 3.
3. If the company wants to pull up your credit history (legally you should be given notification if they do), are any of the entries under your former name? If yes, go to Step 7. If no or they're not going to pull it, go to Step 4.
4. Do all of your references know you by your new name? If yes, go to Step 5. If no, go to Step 8.
5. Is
all of your work and educational history (as well as any relevant certifications/licenses) under your new name (either because you changed your name before your first job or attended the institution, or
all such places have updated your records)? If yes, go to Step 10. If no, go to Step 6.
6. Is any of the work or educational history under your former name something they'd
likely check? (Things they'd unlikely check would be for example decades-old work history or secondary school records once you've graduated from college.) If yes, go to Step 8. If no, go to Step 9.
7. You must disclose that name, or you could run into trouble legally by concealing important information.
8. You'll probably have to eventually disclose that name (or else you may get a work/school/reference check that bounces back because they don't know or can't locate you by your new name), but you could put down something like "will discuss" or "available upon request" if you want to avoid mentioning it when making your first impression.
9. As with the Step 8 scenario you could mention something similar, but this time first mention if asked that you had a name change so many years ago and that chances are the stuff they'd want to check wouldn't be under that name.
10. You probably don't need to even bring up that your name was changed, but if you want to be safe you could put down that no relevant records are under any other name (and they'd generally assume you had a pre-adulthood name change).
This could probably also apply to applications for credit, but start with Step 2 (or Step 3 if there won't be any criminal history checks) and if you end up at Step 5 go to Step 10. Since most employers these days will want to know about your criminal background to some extent I include Step 2 unconditionally.
Sources:
Guidelines on what's legal and what's not for employers to ask, and ways for an applicant to handle dicey questions. A question made by someone who was adopted on a forum on whether or not a name change made as a child is relevant when applying for jobs (which except for the #1 scenario in this post where they trace you back to birth is usually "no"). It should also be noted that having legally changed your name is not the only way that one of these steps may be triggered; if you committed a crime under an alias, or if you're known to references by or have credit under a nickname or other name, they'd need to know that in order for the checks to go through properly (and conversely a legal name change that does not trigger one of these steps, such as the aforementioned adoption in non-#1 cases, is typically not relevant). Since I'm not a professional on this subject matter, don't take this advice as if I was (it's based on research from the sources I mentioned).
ETA: Added certifications/licenses in Step 5.
