It was Marlin that started the "30/30" moniker, I think Marlin did that across the board for all Winchester cartridges chambered in Marlin's rifles.

Remington was sued by Winchester over Remington's use of "30/30 Remington" for the 30 Remington cartridge used in the Model 8 rifle. Winchester lost the suit when it was discovered there was no copywrite on the designation while Remington dropped the use of "30/30 Remington" due to confusion between Winchester's rimmed cartridge and Remington's very similar rimless cartridge. Both sides ended up winners and losers over that fight.