Here's a summary of the article "Meals" written by Professor Gutsfeld (Université de Lorraine) for Der Neue Pauly - if you're serious about Latin or classical studies, you should already know what it is. Unfortunately, it is behind a paywall, so many of us mostly likely will never access this fantastic multivolume reference.
- ientaculum or ieientaculum (breakfast);
- cena (main midday meal);
- vesperna (a light meal in the evening).
Gutsfeld mentions that merenda was common in the countryside and was taken in the later afternoon.
Late Republic - Empire:
- ientaculum (light breakfast);
- prandium (second breakfast without courses);
- cena (main meal consisting of several courses; late afternoon-night).
Gutsfeld also notes that "[t]he rich favoured four or more meals over three while the poor often only had the means for one meal or went hungry."
Since your question is about names of meals and their use, I did not write about food common at those meals nor did I address formal or public meals (e.g. convivium, a private banquet, or comissatio, a drinking party with dances, games, and alcohol).
However, if you are interested in this extensively researched topic, I direct you to the following sources:
Food: see relevant articles in A Companion to Food in the Ancient World.
John F. Donahue has written extensively on this. Also see Dunbabin and Slater 2011, Roman dining, in The Oxford Handbook of Social Relations in the Roman World. Both Katherine Dunbabin (Department of Classics, McMaster University) and William Slater are well-known names/experts in Roman dining (among other things).
All these sources are also subscription-based.