Even people with one "real name" may have slight variations on it that they use. Many people use their nickname and don't show their middle name. If your name isn't written in Latin script, you might have the original script version and a romanised version, possibly even more than one romanised version. If you're Chinese, you might have a Western name alias which you're known by professionally.
I have recently moved to Denmark, and several public or semi-public database systems have had special attention drawn to how my name might be used, and instructions to avoid certain uses. (For example, there seemed to be a special way to register in a municipality under an assumed name, to avoid stalkers etc.)
Not according to the current laws. You may want to change the laws as well. ( No, I'm not cynical. )
https://en.wikipedia.org/wiki/Legal_name#United_States
> Most states in the United States follow the common law which permits name changing for non-fraudulent purposes. This is actually the most common method, since most women who marry do not petition a court under the statutorily prescribed method, but simply use a new name (typically the husband's, a custom which started under the theory of coverture where a woman lost her identity and most rights when she married).[2] Most state courts have held that a legally assumed name (i.e., for a non-fraudulent purpose) is a legal name and usable as their true name, though assumed names are often not considered the person's technically true name.[3]
In the US the different rules for getting a name changed on official documents sometimes leaves people with official documents in different names, so even if you restrict yourself to documents issued by US government authorities a person can have two names.
> I can't show up to a job interview, use a fake name, and claim I'm being discriminated against...
You could if you're in the process of transitioning. (UK; the US needs to catch up).
And it's not a fake name. It's their name. You seem to think that people have this single thing which is their name - that might be true in the US (I dunno) but it's not true in many other places.
And because the US rules for changing names on documents are inconsistent a person may have a passport in one name but a driving licence in another.