That is called an epic catalogue (TVTropes link!), and is used in several old stories.
Part of the point of this specific epic catalogue is that Culhwch is invoking each member of Arthur's court by name ("this boon I likewise seek at the hands of thy warriors. I seek it from [list of names]"). Because Culhwch needs not just Arthur’s help but also the help of his court, it makes sense that he asks each night individually -- it shows that member's of Arthur’s court are respected as individuals. In addition, the catalogue shows the size of Arthur's court.
In general, catalogue’s are used for similar reasons:
By virtue of these three basic qualities, catalogues can be used to at least four different ends: (1) to describe characters of the plot, (2) to intensify the presentation of the events, (3) to foreshadow future events and create suspense, (4) and to provoke or increase the reader's emotional involvement in the narrative.
(Gaertner, Jan, The Homeric Catalogues and Their Function in Epic Narrative)
However, this specific catalogue is also interesting for a completely different reason: it is a parody of epic catalogues and other narrative techniques! If you read the passage carefully, you will see some funny names:
Hirerwm and Hiratrwm. (The day they went on a visit three Cantrevs provided for their entertainment, and they feasted until noon and drank until night, when they went to sleep. And then they devoured the heads of the vermin through hunger, as if they had never eaten anything. When they made a visit they left neither the fat nor the lean, neither the hot nor the cold, the sour nor the sweet, the fresh nor the salt, the boiled nor the raw.
And Gwevyl the son of Gwestad (on the day that he was sad, he would let one of his lips drop below his waist, while he turned upon the other like a cap upon his head). Uchtryd Varyf Draws (who spread his red untrimmed beard over the eight-and-forty rafters which were in Arthur's Hall).
However, there could be more than satire going on in this story. While the story Culhwch and Olwen has humorous overtones, that shouldn't detract from the "sacredness" of it. In fact, in many European stories, humor and seriousness exist at the same time. From Mabinogion.info:
It is crucial to realise the extent to which this differs from modern
narrative-cultural norms, where the comedic and the dramatic are
mutually exclusive. Modern audiences have become accustomed to the
specialised use of parodic humour as a device to undermine, deflate or
dismiss ‘serious’ genres; making it hard for us to understand how the
comedic and the dramatic can co-exist within the same artistic
expression. But such incompatability of genres has by no means always
been the case. Just as the monstrous gargoyle can inhabit the same
cathedral wall as the saintly icon; or the irreverent doodle can adorn
the exegetical manuscript – it cannot always be said that the presence
of humour or whimsy within the medieval narrative was intended to
undermine its psycho-dramatic potency. Indeed, more often than not,
such flourishes signalled a generalised intensification of affect: a
cultural experience in which all emotional registers (wonder,
hilarity, excitement, fear etc.) were simultaneously subject to
Basically, the fact that the story contains absurd jokes doesn't mean the story isn't serious.