Being stealth in a workplace is unfortunately quite dependent on several key factors that are mostly beyond an individual's control. Whether you can be stealth in the workplace depends fully on whether the option makes itself available to you, and while there are steps you can take to make it more likely, there isn't much that can be done to purposefully guarantee it.
A background check may return past names, though this doesn't seem to bother employers much, since the purpose of background checks is to surface major red flags. "Has a past name, no longer used" is not really a red flag, and is in fact quite common. Many background check companies will surface past names used, but no professional background check company will surface "is transgender," because they would be playing with fire over legally-protected medical information. (It would be obscene, for example, for a background company to list the fabled F64.9 ICD diagnostic code on your report.)
So, aside from whether your hiring manager pays attention to past names on the background check... it also depends on whether your past employers and/or references know to identify you by your current name only. They may out you if they do not. You can politely inform them of the name change, but if you also don't want to be out to them, you may have issues facilitating a clean break. They may not understand the importance if they don't know the context, and they may not respect the importance even if they do. Even then, an honest mistake is possible. You will have to assess the character of your past professional references to determine your risk level.
So it is possible to do in the workplace if you get lucky, but only if. Unfortunately, while there are steps you can take, you actually don't have very much control over whether this is a possible option, since it depends entirely on assumptions other people will make about the information they receive. You can do your best on this front, but you should also be prepared with a backup plan if it does not work.