From the outset it should be recognised that Culhwch is not an ordinary mortal, nor are any of the figures represented in this story integrating Arthur with other mythological figures. They are all, in some fashion, euphemisms for former gods. With that said, let us begin with an analyse of Culhwch.
Culhwch means essentially "Swine Nook", from Cil-Hwch. The reason for this is given in the story of his birth, as from the moment of his conception his mother is driven into a state of madness and wanders the countryside. This may well be related to some aspect of the god relating to inspiration and madness. The pig or boar is related to battle and battle fury and there are various examples of Mercury being linked to the pig or boar in Gaul. We also see Lleu and Lug linked to swine. Lleu's transformed spirit is found by following a large pig. Lug's father is killed when he transforms into a pig. Cuchulain also brings a pig to Conchobor to, in the king's own words, "revive him". Culhwch's father is named Kilydd, (modern Cilydd) meaning perhaps "one who retreats" in the sense of the sunset and the evening. It is used in the phrase - o'r goleu i'r gilydd (From dawn till dusk lit, from light to retreat). The meaning of this name on its own may seem senseless, but combined with Culhwch's mother, Goleuddydd, it makes perfect sense.
Goleuddydd has a very transparent meaning "Light of Day". And so the couple Goleuddydd and Kilydd becomes the actual phrase o'r Goleu (ddydd) i'r Gilydd. His parents are actually daylight and sunset, morning and evening. Alternative phrases in Welsh include "o olau i olau" (from light to light) and "rhwng dau olau" (between two lights) so in this interpretation, Gilydd is not darkness but the receding light, and Golau is the ascending or expanding light. Otherwise put, the rising sun and the setting sun.
The father of Kilydd is named Prince Kilyddon. However, Kilyddon is simply the name for the Caledonian forest, and so Kilydd is thus the son of the wood, which is strikingly similar to the etymological name for Gwydion (of the wood). However, the symbolic link goes further. The Caledonian forest was the retreat of Myrddin (Merlin) and other people who were driven mad and was linked to magic and prophecy. It is liked also to flight, where people who went mad would run to and may have derived its name from Cilydd, meaning to flee. So this link to madness may also explain why Culhwch's mother goes mad when she becomes pregnant. The father of Goleuddydd is Amlawdd Wledig. He is also said in several sources to be the grandfather of King Arthur, which is why in the story Arthur and Culhwch are said to be cousins. He is also the grandfather of figures like Gwynn ap Nudd, and usually related to significant figures through his daughters. It is more difficult to give an account of his name, though it could be related to lust. It is also possible he is related to the Amleth of Norse folklore and features in Shakespeare's play Hamlet.
Finally we get to Olwen herself. Her name means "white track" and glosses as one of the many names for the Milky Way "Llwybr Olwen" (the way of the white track). In Indo-European myths, this track is nearly always associated with a significant goddess and though later sources attribute an association with Gwydion, it is of course possible to have more than one association. And as we will see, this may well relate. In Irish myth, which should be the closest to Welsh, it is generally associated with Boann, one of the many names for the primordial goddess of generation, likely from bo-find, meaning "White Cow". Another name given for this goddess is Ethliu, who is cited as the mother of Lug and daughter of Balor. This is interesting because a similar prophecy is told about both Balor and the father of Olwen, Ysbaddaden, namely, that if his daughter should wed, it would mean his death. Olwen is also secured away by her father in a nearly impossible to reach castle, just as in the Irish case of Ethliu.
But we can also trace this idea to Roman & Greek myths. Ops, a goddess of earth and fertility, was wed to Saturn, who feared being overthrown by his children, so he devoured them. Some Roman sources (Hyginus) claimed that after Ops exchanged Jupiter for a stone he made her feed him. Her breast milk squirted out and created the Milky Way. This appears to be a copy of the tale that relates the creation to the Greek goddess Hera, who creates it while feeding Heracles. In either event, it is a significant female goddess which is responsible for its creation.
Ysbaddeden, the giant father of Olwen may mean "hawthorn" or "thorn bush" but may possibly relate to castration (ysbaddu). An overall analysis of these names shows us that we are dealing with figures of celestial origin.