I would say it depends with who you working, if larger distributor or when buying directly from brand they do care where are you going to sell it.
Yes anything official needs company name, thanks.
I'll give you specific example.
Lets say I have got company named Rotfl Electrics Ltd and I'm running retail shop with electronic under same name but then I decided to open second business, let it be organic goods ecommerce retail shop with trading name organicgogo, so I've got 1 company, two businesses. Now, when calling organic goods suppliers for my new organic goods shop, what you think should I say? When I'll say: Hi my name is xxx I'm at Rotfl Electrincs Ltd, they may be suprised how this company could be connected to organic goods, on the other hand I could say I'm at Organicgogo cause they will supply actually my second shop with organic goods, or should I say I'm at Rotfl Electronics Ltd, we are owners of rotflelectronics.co.uk and also organicgogo.co.uk, I'm calling you regarding organics goods as we looking to expand our catalog on our ecommerce retail website organicgogo.co.uk..
I hope it makes better view what I'm trying to ask.