One expression I have come to loathe is "building your brand", and variants thereof, such as "personal brand."
The term you are looking for is reputation.
Even in its original context, a brand is:
A brand (or marque for car model) is a name, term, design, symbol or other feature that distinguishes one seller's product from those of others. Brands are used in business, marketing, and advertising. Initially, livestock branding was adopted to differentiate one person's cattle from another's by means of a distinctive symbol burned into the animal's skin with a hot branding iron.
In short, even in its origination, a brand incorporates the markings and stylistic choices that differentiate one product from another, and thus, by being identified with a particular source, has an associated reputation for quality, a particular kind of product or experience, and so on.
We are not products, and the very thinking that pervades people marketing their brand is at its root materialistic.
We are people. We have reputations, not brands, for honesty or cowardice, virtue or vice, competence or foolishness.
We may present different facets of ourselves to the world, dress up for special occasions, etc., but in the end those should be a reflection of what and who we are, the underlying substance. If you want to appear fit, then get fit. the appearance will follow. if you want to learn something to better fit in with people you like, then learn it.
To mold one's appearance without starting on a foundation of substance is to be hollow.