I'm sure the name will live on if nothing else.
I'm not super eat up about the Remington brand. They are evenly matched in rifles and shotguns both. I'd probably miss Golden Sabre defense ammo the most of anything.
But it's the sub brands they control.
Bushmaster - not personally vested in, but man - Marlin - I'm a total Marlin junkie - can't imagine a world without Model 60's, 336's, or the big bore levers in 45/70. .444 Marlin or .450 Marlin. Remington already dealt Marlin a wallop with quality issues, which I understand they've finally worked through. I sure hope Marlin comes out unscathed.
ETA: Dang - their scope (no pun intended) is wider than I realized.
Remington
Bushmaster Firearms
DPMS/Panther Arms
Marlin
H&R
The Parker Gun
Tapco
Advanced Armament Corp.
Dakota Arms
Nesika
Stormlake
Timbersmith
Barnes Bullets
If DPMS and Bushmaster both went away, that would leave a huge hole in the AR market.
H&R, Tapco, Timbersmith, and Advanced Armament I'd miss.