leading, major, premium, principal, top
the world's leading brand of vodka

famous, favourite/favorite, name, popular, well-known
new
generic
own (BrE), store (AmE)
Supermarkets make a lot of profit on their own brands.
You pay less for the store brand.
own-brand/store-brand products

identity, image, name, value
The company owes its success to brand image.
The company's core brand value is consistency in quality and service.

awareness
leader
loyalty
manager

brand of
a well-known brand of toothpaste

particular, peculiar, special, unique
His designs have a unique brand of stylishness.

brand of
his particular brand of comedy