Generally, it's difficult to answer a question of when did x begin or end and they are forbidden by the rules for a reason, but I will give Rome as an example. Brands(if we by brand mean no more than a mark on goods made my a particular producer) were definitely an established concept by the time of the late Republic. For example, wine jars marked L. Eumachius originally made in Pompeii have been found in France and Carthage. As for your second question, yes, there are many such examples. In Pompeii (probably one of the best sources available for ancient everyday life) there is plenty of advertising. There are plenty of rental and gladiatorial game advertisements, but the others are far more interesting. The quotes ahead are taken from Beard's book.

One rough-and-ready plaque, for example, once attached to the outside of a workshop, seems to advertise the skills of ‘Diogenes the builder’ with images of his tools (plumb-bob, trowel, chisel, mallet), plus a phallus thrown in for good luck.

In the house of Umbricius Scaurus, the biggest garum manufacturer in the town, there were mosaics on the floor depicting jars.

Each one carried an inscription referring to different varieties of fish sauce sold by Umbricius Scaurus: ‘Scaurus’ best garum, mackerel-based, from Scaurus’ manufactory’, ‘Best fish sauce’, ‘Scaurus’ best garum, mackerel-based’, ‘Fish sauce, grade one, from Scaurus’ manufactory'. These were likely a form of self-advertisement.

There is always more to be said, but you may be interested in my previous answer to When did the concept of a “brand” first come up? How did people differentiate products and their producers (if at all) before brands? There is some good discussion with /u/sicundim as well.