Orcs all have basically the same name. Given name, prefix-surname. Very simple, very universal. I like that about the Orcs. Gives them a big sense of community, though not variety, that other races just don't quite have.
Known Orcish names consist of the Orc’s own name, followed by gro-Father or gra-Mother, depending on the Orc’s sex.
This can be seen in Skyrim in the case of siblings Moth gro-Bagol and Ghorza gra-Bagol. These siblings have the same surname, however, which indicates that one of their parents was missing, dead, or otherwise not part of the family.
There are anomalies to this pattern, however. -Largash and -Dushnikh are both surnames of Orcs. Largash is from the Largashbur Stronghold, and Dushnikh from Dushnikh Yal.
One of these characters, Lash gra-Dushnikh, is known to have a mother, but the father is not made clear to the PC. The character is female, and so her surname should be the mother’s name, not the Stronghold. However, the Orc in question had left the Stronghold and her mother, so perhaps she took the Stronghold name as a way to identify herself by tribe while distancing herself from her immediate family.
Elves in general do not seem to use familial names. Altmer and Bosmer are almost universally only given one name. Dunmer have House names, but it is common for the unaffiliated to have one name or a second name that is unconnected to their family. Orsimer have the only clearly familial naming tradition of the elves, yet even so keep it limited.
Identifying an Orc by their parent or tribe serves as a convenient way to make short associations, and can even be used to trace lineage, though this is painstaking. We have not seen much of Orcish familial life, but I believe that their strongly tribal culture means that children are raised collectively, and the patronymic or matronymic serves as a means of identifying which Orc belongs with which parent at the end of the day, though they are all grouped together otherwise.
Stronghold names would be adopted by orphans or those who were casting off their parents.
Now on to the language.
Orcs have their own “language” in Daggerfall, though this is just a value check in the game mechanics, so I am not going to use it.
Orc names are almost always mono- or bi- syllabic. It is very rare for their names to exceed two syllables per name. Notable examples are in Strongholds (Lar-gash-bur, Nar-zul-bur) and a few Orcish names (Dush-na-mub). However, one and two syllable names are the rule.
Next up, phonemes. Every race has a subset of the common alphabet from which they draw their typical names. Orcs favor oral consonants. They are not guttural, but also rarely labial. Consonants such as D, K, Z, G, N, R, and L are the most commonly used. All of these are formed by manipulating the shape of the mouth and the position of the tongue.
Interestingly, the vowel E is rarely encountered in Orcish names. On the UESP page Lore:Orc_Names, the letter E occurs in the names all of four times. I is slightly more common, but not by much. A, O, and U dominate the vowel population, and never occur as diphthongs. Y occurs solely as a consonant.
If you need to make an Orcish name, I recommend perusing the UESP page. Combinations of consonants, with vowels placed to make syllables so the name can be pronounced, are the norm.
From general observation, feminine names have more vowels and syllable breaks, and less consonants per syllable, than do masculine names. The name I use most, Krognaz gro-Makoza, is male for the given name and female for the surname. I don’t know how well that came across, but I’m rather proud of it.