1) He started with Stark Industries, which evolved into Stark International over time. He lost Stark Int'l when Obadiah Stane forced him out, creating Stane International. After he crawled up out of the bottle, Stark formed a small design company with Rhodey and two friends called "Circuits Maximus". Stane destroyed that business too, but Stark finally disposed of Stane after that.
Tony rebuilt his company as Stark Enterprises in California, which he ran until his deaths in The Crossing and Onslaught. SE was bought out and became Stark-Fujikawa after that, and when Tony returned he made a new troubleshooting company called Stark Solutions. After several years he eventually reclaimed the Stark Industries name and abandoned SS. Stark Industries was crippled in a massive attack by Ezekiel Stane and the Skrull invasion.
Currently, Stark is once again running a small firm, now called Stark Resilient.
2) The term "StarkTech" has only been coined in the last few years, but assuming it applies retroactively to any armor based off of Tony's designs...
-Iron Man (Tony, Rhodey, Eddie March, Bethany Cabe, Happy Hogan, and Carl Walker have all worn the suit)
-War Machine (Rhodey and Parnell Jacobs)
-Spider-Man and the Scarlet Spiders in the Iron Spider suit
-Beetle, Controller, Crimson Dynamo, Titanium Man, Firepower, Stilt Man, Mauler, Raiders, Force (all from Armor Wars)
-Blizzard, Living Laser, Vibro, Chemistro, Melter, Firebrand, Whirlwind, Ezekiel Stane, Sasha Hammer (all using Stane's reverse engineered StarkTech)