Innershield is definitely a Lincoln trademark, but my understanding from the very limited search results was that the Lincoln trademark didn't come into play until a few years after Arthur Bernard called it Dualshield. Lincoln expanded on it and developed a FCAW wire that didn't require external shielding.
The following was taken from an article in October 2007 edition of The American Welder , “A Brief History of Filler Metals”
"With the introduction of welding with CO2 shielding gas came other filler metal inventions, notably the precursors to today’s flux cored wire. Attributed to Arthur Bernard in 1954, who dubbed the process Dualshield®, flux cored arc welding (FCAW) began with the creation of a flux cored wire, similar to those manufactured today. The flux itself generated shielding gas, but an external supply of CO2 was still necessary to protect the weld pool. The development of a self shielded welding wire in 1959 would eliminate the need for an external shielding gas supply, and it was therefore called Innershield®"
Here's a link to that article........
http://files.aws.org/wj/2007/10/wj200710/wj1007-113.pdf