If you are making it for cafes, then they will never allow your brand. However, if you are selling it outside the cafes to someone else, then you can use your brand,
Completely wrong.
Never been in a cafe where the cakes etc were branded. The only brand the cafe is going to want to promote is their own.... unless you are willing to pay them/give them a discount to advertise your brand.
Also wrong.
OP - as someone above said, this is time to have a conversation and get talking. For a start - do YOU want to be associated with that place? Do you have a premium product that fits with their venue? Or are they a greasy spoon and people might associate you as being cheap/low cost. Are they the kind of place that is happy to make 10p on every cake they sell and devalue your prices elsewhere?
If you do want to be associated with them, what can you also offer? Do you have a good social media following so you can promote "XYZ cakes now available at ABC Cafe, go give them a try!". Is it going to entice people in if they see your poster in the window or encourage them to order if they see your name on the menu?
For example (we sell pies, but similar scenario) we have been approached by some establishments in the past that are known for either poor hygiene, low prices, reheating food etc. In some cases, we have refused to supply them. In other cases we have supplied them at a low price on the understanding that they do not promote it as our product, and they don't get any additional support or advertising etc, they're just buying a product and that's it.
Other establishments we work really well together - so we provide signage for outside and in the window, We promote them through our social media, we have developed special one off pies specifically available at one location and promoted that people have to go there to try them. We supply a great local quite high-end pub restaurant and we're proudly emblazoned on their menu because it's not just "another steak & ale pie" - it's made half a mile away with meat from the butchers just up the road. So it fits really well with their ethos and local produce thing.
In return for this kind of relationship, they often recommend us or encourage people to visit our shop to try more of our produce. One place takes customer orders for frozen produce and items that they don't stock and we deliver them there for locals to collect. It's resulted in conversations with their other suppliers and talk of collaborations together or working together to supply "leads" for customers we each have.
So there's definitely a possibility there and the whole supporting local and reciprocal support of other small businesses is a big thing at the moment. But that has to come from both sides of the table.
And, having said all that, there is still the possibility that they just want people to believe they are getting a home made (on the premises by them) cake and if that's the case you have to accept you're a 3rd party supplier, make sure the business is worthwhile to you, and get on with it
