The term legal entity is sometimes used:
to refer to a juristic person, an artificial entity that the law treats for some purposes as if it were a person, such as an incorporated organization.
as a general term to describe all entities recognized by the law, including both juristic and natural persons.
What is called a juristic person is also called a legal person, an artificial person or a corporation (I use British English unless otherwise indicated). Company law books often write of corporate personality (this may be corporate personhood in the USA, since Wikipedia also tells me that corporate personality is another term for multiple personality disorder, which sounds more like a partnership than a company).
The first meaning would include a private or public limited company, a GmbH, an AG.
The second meaning would include all those, but also natural persons, and even groups of persons such as partnerships.
The context should make the meaning clear, however.
This old ProZ question on translating legal entity into German illustrates the pitfalls of legal translation:
Ein schöner Ausdruck! Reicht aus, hier von einer "Unternehmung" zu sprechen?
Company code (Buchungskreis): this is a legal entity to which accounting data refers. There are three company codes:
A010 Aniello Entsorgungswerke
A020 Aniello Klärwerke
A610 Aniello Dienstleistungen
The name 'Aniello' was just a pseudonym for these entities. I suspect myself the term was used in the second sense. But no-one even asked whether these were companies or partnerships - they may have been municipal corporations - and yet juristische Personen was the answer selected (still, it only got 3 points out of the possible 4!).
However, I can't help thinking Volkmar Hirantner's suggestion of Mandanten was spot-on. Mandant is a term used in accounting - for instance, if your accounting software is mandantenfähig (multi-client-capable? multi-user-enabled?), you can use it for more than one of your clients.
This sort of thing is one of the reasons why we don't rely on dictionaries.