A. Compounds containing only carbon and hydrogen elements in organic matter are called hydrocarbons, so rosmarinic acid is not an aromatic hydrocarbon, so A is wrong;

B. According to the simplified structural formula Know: The functional groups contained in this molecule include phenolic hydroxyl group, carboxyl group, ester group, carbon-carbon double bond, and benzene ring, so it is correct;

C. This molecule contains phenolic hydroxyl group, and the number of phenolic hydroxyl groups on the benzene ring is ***6 mol of hydrogen atoms in the and para positions can undergo a substitution reaction with bromine, that is, it can undergo a substitution reaction with 6 mol of bromine, so C is wrong;

D. 1 mol of rosmarinic acid contains 4 mol of phenolic hydroxyl groups, 1 mol of carboxyl group, 1 mol of ester group, 4 mol of phenolic hydroxyl group requires 4 mol of sodium hydroxide to react with it, 1 mol of carboxyl group requires 1 mol of sodium hydroxide to react with it, and 1 mol of ester group requires 1 mol of sodium hydroxide to react with it, so 1 mol of rosmarinic acid can react with up to 6 mol of NaOH. The aqueous solution reacts completely, so D is wrong;

So choose B.