Pesan is the root/base form of memesan. We know that verbs with this prefix, me- are transitive verbs; they need an object (in this case, makanan). In conversations, some verbs may lose their me- prefix without a change in meaning. This often sounds less formal. Very often, the prefix causes sound change when attached to a base verb. For example, if the verb starts with "p", it "dissolves into "m", so pesan becomes memesan.
Prefixes and affixes are very important in Indonesian, since they attach to other words and change their meaning. So it's not necessarily a new word, but reusing a known word :)