A few points I'd make here:
Most of the food you eat in the mix is going to either be, or contain VS patented plant and animal products. Tony's Pizza? ViriiSoma products. Soyanuts? ViriiSoma products. Some shitty food vendor hawking kung pao chicken? ViriiSoma products.
The medical treatments in CGH and FullerMed. That's ViriiSoma SkinGraft Spray™, Viriisoma Universal Antiseptic™ and ViriiSoma Sticki-Band™.
That shipping container you live in inside XpressHeights is a NeoTrans FreightCrate™ box. Your apartment building constructed out of 97% recycled PRI RockCrete™ with nice PRI Plasti-View™ windows.
The DynaFiber™ clothing you wear, the patented food you eat, the buildings you live and work in, the Chyen™ you earn and spend. It's all corporate.
Unless your character is walking around in pelts and subsiding off dogmeat and acid rainwater, there's literally no way you're escaping corporations owning everything about you. Have you died? Your character itself is a Genetek RealU™ Clone. Are you, yourself, a product? Chances are, you absolutely are.
Branding things in the mix would certainly give people good RP props to work off from, but I can't tell you the number of times I've explicitly RPed handing people New Light Media HoloChyen™ and have gotten weird looks. This is something you can enrich your RP with. Invent products and match them to an appropriate corporation. Bring it into your RP, and pay it forward for others. Every bit helps.