Goblins

In the Forges, goblins live very deep underground, and have one of the few unitary kingdoms around. They are currently engaged in a power struggle for the crown; the goblins characters one might see around are often refugees or exiles, or else raiders raising funds for their own civil war.
The centre of the goblin peoples of the Forges, is Five Bells, so called because it consists of five vast interconnected caverns deep under the surface. Five Bells is the capital of the goblins' kingdom, or possibly most of the kingdom itself, but its nature, size, population, etc. are not known to outsiders.
There are also some isolated goblin communities living along the Small Coast, feyward from Malfa. These people are called sea goblins, not because they're aquatic but because some of them fish right out on the sea, in boats, which is very unusual for goblins.
Goblin ancestor worship, and in particular the use of ancestor relics, is one of the reasons goblins are considered "barbaric" by other peoples.

Goblin Names

Most surface-dwellers don't do well pronouncing Goblin, so the convention amongst goblin travellers/settlers is to use whatever the literal translation of their name is in the local language. This is also because goblin names tend to be very simple, taken from common objects or phenomena. Billy is Billy's full name; he's named after billygoats, it has nothing to do with William. Hye's full name will turn out to be Hyacinth. It might be pretty common to be named after a culturally important food crop, like Ginger or Beet. I don't know if Lorenzo remembers or ever uses his birth name.
Hyacinth's and Billy's names in Goblin are Nchasgh and Jngugk, respectively.
Amongst many goblin peoples, only aristocrats have second names. This is more like an honorific or cognomen than a family name; a person adopts a name based on their accomplishments. By custom, children use one of their parents' cognomens until they achieve enough to choose one of their own.
In the most powerful families, this has resulted in cognomens becoming hereditary, since being a professional descendant is an accomplishment all by itself. Generally speaking, it's considered a bit embarrassing to keep using your parent's cognomen; goblin high families mostly assume this doesn't apply to them, but every once in a while someone will adopt a third name, as a personal cognomen. For instance, the goblin noblewoman Lemon Grim the Mole is thus called because Lemon is her personal name, Grim is her family cognomen, and "the Mole" is the personal cognomen she was given for her actions. In different contexts, she might also be called the Mole Lemon or the Mole Grim. (She was named the Mole by people who think she is inquisitive, dogged, and an irritating pest).
Goblin plebs with the same name as someone else will generally use some qualifier nickname to distinguish themselves, like Younger Lizard or Skinny Carrot.
(Actually Goblin has many names for different types of lizard, that don't translate well into other languages. For instance, "Transvolcanic Alligator Lizard" is a common name for girls in Five Bells, sort of.)