Some trans people live in a way that is often called "stealth." That is, they are not out as trans to most (or perhaps any) people in their lives. Most trans people change their names, but some have moved to different towns where no one knows them, taken new jobs, and have not come out to folks around them.
Most trans people early in their transition, some who are later in their transition, and many non-binary and gender-expansive folks, don't "pass" in the standard way to fit into society's binary categories, and that can be really challenging, depending on where they live. These folks often face misgendering, people's lack of understanding, or even outright hostility toward their gender.
For those of us that have passing privilege, unless one always wears an "I'm trans" t-shirt on, we live some parts of our lives in stealth mode. The decision how and when to come out to people is sometimes a challenging one. I am obviously publicly out as trans, and if anyone googles my name, it will be really obvious, but I don't tell everyone I know all of the time. I have casual relationships with relatively new acquaintances who, unless they took the trouble of googling me (if they even know my full name), wouldn't know.
And at the moment we decide to come out to someone, it is always a question of their reaction - how are they going to react to knowing I'm trans? Will I lose my connection with them? Will they respond with violence?
The elements of figuring out whether to live in stealth mode, and/or how many people to tell in our lives, and how to come out is a complex one. It's based both on practical issues as well as our own internal process. It's important to parse those out - what are the things that are necessary for our life and survival as a trans person in this generally transphobic, gender binary society, and what might more be from a sense of shame, or lack of self-worth? Are we not disclosing our identity as trans out of shame, or out of necessity?
I also want to add that some people who live as the opposite of the gender they were assigned at birth don't identify as trans at all. And that's fine. Inhabiting your identity as whatever the gender you are is what's important. But it's also important to work toward learning to love where you've come from - because all of that is still a part of you.