Eelwasser and Slug-O-Cola are both brand-name products made by the Ferengi, presumably by for-profit companies or corporations. D'Kora class ships are also made by a Ferengi company. And one would think Ferengi society would have abundant companies and corporations.
There are several corporations (including Yoyodyne) listed in Mr. Scott's Guide To The Enterprise as involved in starship construction, and I seem to recall it being said that the ship's computer on the NX-01 was made by Apple, but I can't recall a source for that.
Galactic Mining Company was shown in the TOS episode "Where No Man Has Gone Before".
BioResearch Corporation was mentioned in the FASA RPG sourcebooks, as was the Orion company, Crecent and Trefoil Developments.
House Ozhpri and Chateau Picard both seem to be fairly large wineries. Not sure if they would still count as individuals' businesses, but I wouldn't think so.
Trans-Universal Shipping was a company that Chekov worked for in the TOS novel "The Fearful Summons".
Trilateral Broadcasting Company is based on the planet Viden in the 4th issue of the TOS - Year 4 comic series.
Turok and Sokor were rival shipbuilding companies on Qo'noS in the KE novel "A Burning House".
There was a car company that made a car called the "Jupiter 8" on Magna Roma, and presumably the cars the Iotians used were made by a manufacturing company, as well - both in TOS, of course.
The Earth Broadcasting Company was a news company with representatives onboard the Enterprise-B during her maiden voyage.
The Jupiter Mining Corporation, Diet Smith Corporation, and the Diva Droid Corporation had offices on the Promenade of DS9, as did the Sirius Cybernetics Corporation, which was also mentioned in "The Schizoid Man" episode of TNG.
And the National Biscuit Company, or Nabisco, was mentioned in the final episode of TOS as depicted on Saturday Night Live.