Agent is a term that can be applied to almost any non-Flower member of the PPC. It is not, however, universally used. The janitors and cafeteria staff are very rarely referred to as agents, despite technically, as members of the Department of Operations, being exactly that. However, the word is not just applied to members of the Action Departments—Agent Imbolc Telyan was in the Department of Finance, while Agent Quen works in the Department of Personnel.
While the word agent may be used in general, and as affixed to a name (e.g. "Agent Jay Thorntree"), most of the individual departments have specific designations for their agents. Agents of the Department of Mary Sues are assassins, while those of the Department of Implausible Crossovers are untanglers or disentanglers (not to be confused with the Disentangler). However, referring to "Assassin Acacia Byrd" will only get you confused stares.
Occasionally, particularly during the era Jay and Acacia were partnered, the title "constable" was given to agents in the DMS.
In the very beginning of the PPC, the agents were, in fact, Flowers. At this time, before the growth of the internet, the Organisation sent them out into the Word Worlds in teams of three. The arrival of the first non-Flowers (known to be, in order, Makes-Things, Anya, Elisabeth, and Montgomery Osbert III) into Headquarters coincided with an increase in the volume of fanfic, and so most of the Flowers retreated Upstairs and let the humans take up the slack; while some Flowers, such as the Wallflower, have continued to work as field agents, they are the minority. Nowadays, agents go about in pairs, or occasionally individually. There are still a few trios, but these are often for training purposes.