I have some experience in the civilian world of defense industries. (BTW - If you value your soul and your mind stay far away. I just finished up 6 years in hell and am now celebrating my 1st aniversary of freedom and joy being a for real engineer again that can fix things)
First off you have your pre-employement criminal background check. Which is really a public records search. Name changes are part of the public record and it will get turned up. Since there is no SS number associated with it, there is wiggle room. But if name, address etc of old/new you match, then not so much room. Which then leads to actually what gets reported back to the employer. Discrepancies for sure I think. Lack of inconstancies I think will fly better. All HR wants is CYA that you are not a No-Goodnick.
OK Hurdle one passed. Except.... Name, SS Num, and Gender comes back mis-matched from SS. Or, was that taken care of? Medical Insurance will also catch that.
If the time comes for a DOD or DOE security clearance don't worry. Since it is illegal for anyone with a clearance to say they have one, to about anyone, let's say I have heard from people who have heard from people who know things. One of the things they know is that there are transitioned TS's with clearances. I cannot say for sure but I am fairly confident the rules pretty much say they can't bounce you for that anymore.
Also, keep in mind about any employer of more than like 20 heads these days all have their boiler plate Non-Discrimination policy. Most cover sexual orientation as well as gender expression. But this has not stopped the company from having medical insurance policies that do discriminant against anything Gender related. (My trump card if or when that day comes. Feel free to use it)