Back in 2013 I posted here (https://www.susans.org/forums/index.php?topic=144386.0) about how the revised (at the time) Form I-9 (https://www.uscis.gov/i-9) (used in the U.S. to verify work eligibility) had the side effect of implying to transgender people that they had to "out" themselves by providing their birth given name in the revised "Other Names Used" field even when not practically necessary (before that the field just asked for "Maiden Name" which despite the semantic issues that term has to some women effectively referred to only a former last name changed due to marriage and not a former first name). Since then I and some transgender people have tried to get this issue fixed. They didn't provide a meaningful response until about a year ago when they took comments (https://www.regulations.gov/docket?D=USCIS-2006-0068) on regulations.gov (https://www.regulations.gov/) about another form revision; here the field was changed to "Other Last Names Used" which solves the aforementioned problem*. That new form has finally been approved and released for use by employers.
*During that comment period NCTE (http://www.transequality.org/) posted their recommendation that the field should be optional unless for example the employee presents documentation with or their Social Security record (when using E-Verify) still has their old name on it, even when it comes to last names (since some transgender people change their last name to make their past harder to trace down, and although requiring them to provide that last name won't immediately out them like their old first name would, it'd make it easier to run such a search especially if their original last name is not common enough to dilute the search results). NCTE did not get that wish, with USCIS citing that making it mandatory for employees to provide all other last names used is necessary for identity verification purposes. My original suggestion was similar, keeping the "Other Names Used" designation the same but providing an exemption when providing the former name could create privacy and/or discrimination issues and not pragmatically necessary to properly verify the employee (which in addition to transgender people would also apply when for instance someone changes their name to be less suggestive of their race/religion/national origin due to discrimination issues, or someone was adopted as a child or the name change was sealed due to being a DV, etc. victim) - that idea was probably turned down because it'd make the instructions a little longer. The form as revised addresses those concerns only when just the first/middle names were changed - but at least that's much better for transgender people, and just as good for those who kept the same last name (and those who don't have gender issues but disliked what their parents named them and had their given name(s) legally changed get a side-effect perk). Another factor behind the change may be that people would frequently put a nickname, etc. in the field when its intent was for former (now just last) names.
With many of us in a pessimistic mood after the elections and how they turned out, at least here's one move in the right direction (although it's really reversing a bad change).
I'd just leave that space blank. I've managed, and in the nick of time, to change every document that could possibly identify me including the following:
Birth certificate
Social security
Drivers license
High school diploma
High school transcripts
College degree
College transcripts
Employment records
Amy - Your logic may work for instance when an employer wants to check your background, but the I-9 is different because it's a government form designed for their purpose of identifying legal vs. illegal workers. On the now lame-duck form the guidance regarding the "Other Names Used" field was rather vague* and the space had not been adjusted to fit a longer full name (so a TG might have been able to pull off putting something like just their old initials or last name if different). On the new form the guidance is more precise, one of the form versions is a "smart" form which among other things won't accept an incomplete form (they say to put "N/A" in the field if you've not used other last names), and the penalties on the employer for form completion errors have been heightened. *This also meant there was ambiguity about whether or not nicknames, truncated hyphenated names, etc. had to be included.
I think why USCIS came up with the compromise they did was:
1. Legal changes to the last name are very common (e.g. marriage/divorce) while official changes to the first name are less frequent (and when done are more likely to have documentation changed in a timely matter than for example how some women when marrying are slow on switching their documents).
2. There is more likely to be an issue of the former name itself giving away why the change was made with first name changes than last name ones. Obviously there are our cases as well as cases like where their parents went "crazy" with naming their children (which may have also factored into USCIS's decision, citing transgender people as well as other more general circumstances where discrimination is possible for their decision). While the issue is not nonexistent with last name changes (e.g. immigrants "Americanizing" their names, religious conversions, etc.), the bulk of last name changes are due to family reasons (which other than marriage/divorce include adoption, paternity issues, family associations, etc.) where although the person may prefer not to disclose it for personal reasons just giving out said former last name would not indicate the reason for the change.
3. When someone tries to change their name for illegal or fraudulent reasons it's less common for them to change their first name alone (more often they do the full name or just their last name).
I hope Mike Pence doesn't reverse this!