If you're transgender and a prospective employer wants to check your references, there might be some confusion if you were known by a different name and gender at your previous jobs. This is a tricky issue for transgender applicants, especially those who are not interested in being "out" as transgender and would rather simply be another man (or woman) in the workforce.
You can go to court to get an order changing your name, which allows you to get new government identification documents with your correct name and gender. Many states also allow you to get a new or amended birth certificate, reflecting the gender with which you have always identified rather than the gender you were assigned at birth. (Typically, though, you must show that you have undergone sex reassignment surgery.) However, from a practical perspective, there's not much you can do to change people's memories of you before you transitioned.
From a legal standpoint, the Supreme Court ruled in 2020 that employers are legally prohibited from discriminating against workers on the basis of gender identity (Bostock v. Clayton County, 590 U.S. ____ (2020)). As a result, prospective employers may not refuse to hire you or consider your application because you are transgender.
Practically speaking, failing to clarify your name change and gender transition with a prospective employer could lead to confusion. A potential employer could call a prior employer, ask for information about "Sarah," and be told that no employee by that name has ever worked for the company. This isn't going to help you land a new job, especially if your former employer would have given you a good reference. Even if you would prefer not to reveal your transition, it's a practical necessity here.
To figure out how and when it's best to have this conversation with a prospective employer, you might want to check out some of the great online resources for employees who are transitioning at work or looking for work during or after a gender transition, such as the Transgender Law Center or the Transgender Economic Empowerment Initiative.