Maya society was organized in city states and clans and possibly other entities. Each of these naturally provides its own narratives and mythology from which names would often be chosen. It is therefore common that multiple individuals from similar contexts, e.g. multiple rulers of the same polity, would have similar or identical names. For instance, several of Palenque's (Baak, Lakamha) rulers were named K'inich Janaab' Pakal, while several others bore the name Ahkal Mo' Nahb and still others K'inich Kan Bahlam.
The clan name (e.g. Mat, a clan from Palenque) occasionally formed part of the name. For instance, another one of Palenque's rulers is named Ajen Yohl Mat. However, this is not a general rule, and it appears that occasionally individuals not belonging to clan Mat would also bear that element Mat as part of their name, e.g. in the case of individuals that had ancestry from clan Mat though not belonging to this clan themselves. The details of this are not currently well-understood. For a discussion of this particular example, see pages 56-60 in this paper about the rulers of Palenque.
Titles like Ajaw (Lord), K'uhul Ajaw (Divine Lord, King), etc. would often be added to the names. Such titles would, as I understand it, typically include a description of what the individual was Lord or King and would follow the name. Title and description would be combined into a single logogram. The same is true for the name. For a description with examples, see e.g. page 8 in the paper referenced above. Note that Mayan writing did not prescribe a particular orthography but allowed any number of ways to phonetically and symbolically combine elements to convey what you want to say.
Names may include otherwise unfamiliar characters, as is the case for the names apparently referring to foreign invaders from the Mexican highlands, such as "Owl that will strike" (the Mayan reading of which is unknown) or "Fire is born!" (read Siyaj K'ak').
Edit: I forgot to add, that even though the question refers to names of common people, I am talking about names of the nobility. Very little is known about the classic-period Maya in general, even about the nobility. What little we know is from inscriptions, which are exclusively from the perspective of the upper classes and mainly about the lives of the upper classes. We do not have any texts about naming customs, so everything we have is inferred from names. If naming customs for commoners were markedly different is impossible to know. What we know about the nobility is simply the best approximation of naming customs in general that we have.