Is there any reason certain names end up being used so repeatedly in the Ulster Cycle? Like, I remember reading some translations of The Wooing of Emer+Cú Chulainn's Training with Scathach, and the name Cett/Cat appears 3 times; once as one of Emer's brothers, once as one of Scathach's sons, and once as a soldier fighting with Aoife. Is it just a translation thing or is it not actually deep and it was just a common name? Sorry if this question seems a little stupid. Thank you for your time.
Interesting question! I've been thinking a lot about names recently, particularly those that repeat, so this coincides well.
A lot of the time, I think it's simply that they're common names. There are a zillion guys called Ailill (sometimes within the same text), every other random maiden seems to be called Étain, and I lose track of how many Eochaids there are. Whenever you get an index of names, as you sometimes do for longer texts where a lot of characters appear, you find yourself scrolling through half a page of the same name. If you're lucky, they'll be distinguished by epithets or patronymics. If you're not, good luck figuring out which Lugaid you're supposed to be looking up...
There are some names that only come up once, like Cú Chulainn, but for the most part, I'd hazard that it's more common for there to be multiple characters with a name than for it to be wholly unique.
Now, sometimes this is a plot point. Recently, I've been working on a tiny fragment from TCD H.3.17, concerning the seven Maines. The seven Maines, if you haven't come across them, are the seven sons of Medb and Ailill, all of whom have the same name (but different epithets to distinguish them). In this case, there's a reason for it: Medb renamed all of them because when she asked a druid which of her sons would kill Conchobar, he prophesied that it would be Maine. Realising she didn't have a son called Maine yet, Medb took action to fix that. But! She wasn't precise enough in her question. Maine Andoe does kill a Conchobar... but it's a different one.
So here we have a story that not only involves seven people called Maine, but also two people called Conchobar, and that overlap is central to the plot. But this fragment seems to be an excerpt from the longer text Cath Boinde... where there are two guys called Eochaid and that's not a plot point whatsoever. Eochaid Feidleach and Eochaid Dala just happen to have the same first name. Even within the same story, repeated names both do and don't have meaning.
The Maines aren't too unusual, even if they're one of the only groups I know of where there's an explanation for their names: there are a lot of lists of people with the same name. In the Táin the largest groups of same-named warriors are ten people, I think ("Ten Fiacs, ten Fiachas, ten Feidlimids"), although three is a pretty common number there and in Togail Bruidne Da Derga. But in some of the later (early modern) texts, we get groups of up to three hundred: "Ferdia son of Daman with three hundred Ferdias in his train; Fraoch son of Fidhach with three hundred Fraochs [etc.]" (Táin Bó Flidais II). It makes you wonder whether they made them all change their name, or whether they just had a highly selective job interview process with only one question...
It's clear that names recur a lot even within the same texts, but what about across different texts? Well, looking at the example you asked about, it's worth noting that The Training of Cú Chulainn is a later text that derives from The Wooing of Emer, so that may also result in some overlap or borrowing of names -- even if it's for different characters. But often the reason a name is common is to do with the meaning of it. You get a lot of names with the Cú or Con element at the beginning because 'hound' was evidently a comparison made for particularly fierce fighters. You also get a lot of names with the 'Fer' prefix -- Fer Diad, Fer Baeth, Fer Logain, etc, and 'fer' just means 'man'. So names that mean things are bound to recur.
What do these names mean? Well, I'm away from my books and library access at the moment, which makes it a little tricky to verify which spellings are used in the original Irish of those texts -- Cat and Cett would be distinct names, but I'm also aware of at least one spelling of Scáthach's son's name as Caid, which would be different again. (Caid means 'pure, holy, noble', which would maybe place him in opposition to her other son Cuar, meaning 'crooked, bent', although it usually means in the physical rather than moral sense -- and I'm not sure where the Caid spelling comes from as I've only come across it in translation.)* It looks like it's usually spelled Cet in Tochmarc Emire (but one of the manuscripts also says 'Scathqu' at one point, so I Don't Trust It). The most famous Cet is Cet mac Mágach, but 'cét' has a bunch of meanings -- it can mean 'first', it can mean 'a hundred'... it's a solid name for a firstborn son, so maybe that's why it shows up so much. One of the MSs of Training uses Cat, which is harder to pin down -- it could just mean 'cat', although that seems unlikely, or maybe it relates to 'cath' ('battle'), or maybe it's an early modern scribe getting confused about his vowels, I'm not sure.
This is... getting very long, and not saying much, so, the short version is: Sometimes Names Just Show Up A Lot. And the scribes and authors are evidently aware of the potential for confusion and plot points with regard to this, as the story of the seven Maines proves, but at other times, they throw repetition at you and leave you to figure it out. But a lot of the names that show up very frequently do so because they have a meaning, one that may relate to the characters' physical traits (so many fair-haired Fionns!) or their skills or even just their birth order.
I hope this was... useful? Sorry, I feel like I just threw a lot of words at you when you were probably looking for a quick answer. You happened to catch me at a time when I'm immersed in thinking about names in medieval Irish lit, so the infodumping was inevitable!
* Note that manuscript spellings are often wildly inconsistent, so the same name might show up as Cet, Cat, Caut -- without translating fully and getting context, it's hard to figure out whether they're all the same person, and right now I'm just scrolling quickly through editions, so I apologise if I've missed anything in that regard.