The title of the article is evidently draw from the quote the article is opened with (from a court on this issue), and seems to me like a perfectly reasonable use of the English language in that the article is specifically addressing the "legal name" as a commonly understood concept, not in some abstract sense of the meaning of the words.

As the article points out, one of the fundamental issues here is that while "legal name" is commonly defined as "the name on your identification," it is not unusual for people to have different identification documents with different names. While the US government has made an attempt to significantly curtail this happening, it remains the case for many and I happen to be one such example without even an unusual story. It's also not unusual for courts, perhaps the definition of "legal," to use names other than the one on identification when recognizing parties---indeed, the courts are far more flexible on this issue than the DMV. While a court order is required to satisfy certain requirements the entire system is very ad-hoc and not well defined, and there are multiple circumstances in which it's possible to e.g. cause a state government to issue identification with a different name without a court order (and this even happens accidentally or for incidental reasons with some frequency). Much of this flows from the fact that the United States does not maintain any official registry of persons, but for various reasons that's usually viewed as undesirable.

As recently as the mid-century it wasn't unusual for people's birth certificates to not even give a name, if the parent's hadn't chosen one yet when the doctor filled out the paperwork. For many years this almost never caused problems, but today's aggressive approach to identity verification has lead someone I know to have to get a court order in order to renew their driver's license with the same name it had previously shown. And of course the same name in SSA records, which is usually the closest thing there is to a "standard."

If you start working in an environment where badges are issued based on Federal standards for a "legal name" you will start noticing just how frequently these kinds of things come up, and it's nowhere near as simple as being based on "birth name" or immigration records. The end result is that things like being issued a staff badge with a different name than the one on your driver's license are not really that unusual, because it turns out that when you actually look close no one actually agrees on what your "legal name" is (the article is centered around exactly this point). In practice most everyone just considers your "legal name" to be the one on whatever dataset they're working against, whether that's birth certificate, state-issued ID, or social security registry. There are many cases where these are different, despite the best efforts of REAL ID!

And on top of that technical constraints can lead to really stupid situations like one I ran into years ago in which an employer (not even a government one) refused to issue them a badge with their name written in any way other than having their first name consist of multiple names concatenated (without spaces) and then truncated in the middle of one of them, because due to DMV system limitations that was how their name was printed on their driver's license and, in the sense of an organization that has never really thought this out, that made their "legal name" "TAYLORBYRNEMCCAR". I think everyone agrees that situation is dumb but it's honestly the tip of the iceberg of people getting their name represented in weird ways because of organizations trying to enforce this concept of a "legal name."