Alarith is the only merchant in the Denerim Alienage. During the city elf origin he will offer advice to the Warden. During the Unrest in the Alienage quest, he will update the Warden on the present situation of the Alienage.
Alarith will offer items for sale in the first discussion, (he does sell some trap plans). Ask what he has for sale first, because after any other question he will tell you the store is closed. It does not open until Unrest in the Alienage quest has been completed. (NOTE: this was as an Elf mage, but if asked for information first there would be no opportunity to see his wares. This may be a bug in the dialogue tree more than anything, so some confirmation would be nice)