Even a “legal name” can be different things in the same legal jurisdiction, or not be a concept that really exists at all. I’m in the USA and my birth certificate doesn’t have distinct first, middle, and last name fields. It’s just a single line with my whole name typed out.
That's sort of my point. The Legal Name field is a single field, like it apparently is on your birth certificate. It's just a byte-stuffer identifier filled with something that can be used by the business for any legal forms that come up.
The individual parts inside don't, and shouldn't, matter.
Also, long-standing common law precedent in the US is that people can call themselves whatever they like for any reason at any time as long as it's not with intent to deceive or defraud. This is the basic principle behind, for example, businesses run using stage or pen names (see: "Prince").
Even stranger is that birth certificates are the foundation for all identity in the United States, yet there are >14,000 forms and very poor standards around them.