What is the formal name for animals with full digestive tracts, by which I mean a mouth and an anus, and what is the classification for animals that have a single hole for exchanging food and waste?
Animals with a single hole do not form a monophyletic group: metazoa > eumetazoa >bilateria almost all have separate mouth and anus (except notably flatworms which is one reason it does not form a monophyletic group).
As species are not grouped in monophyletic groups by what they don't have (eg. invertebrates do not form a monophyletic group while vertebrates do) there is no particular group. Eumetazoa before the bilateria have a single mouth-anus.