The name “Berrjod” comes from Old Norse “Berurjóðr”, which is composed of “bera” and “rjóðr”. The latter means “glade”, and the former is speculated to be the name of a river. But where the river name comes from is less clear. It could be from the verb “bera”, meaning “to carry”, or it could be from the noun “bera”, meaning “female bear”. Either way, it’s not surprising that “Berurjóðr” would become “Berrjod” (pronounced [ˈbǽʁju] locally) in modern Norwegian.
At one point, the modern form was likely mistaken as a corruption of “Bergljod”, a compound of “berg”, meaning “mountain”, and “ljod”, meaning “sound”. However, this would have had to come from “Berghljóð” or “Bjarghljóð”, which are not attested, to my knowledge. This misunderstanding of the name was written down in regular Dano-Norwegian spelling as “Berglyd” (pronounced [ˈbæ̀ʁɡˌly͑ːd] locally).
Both names are in common use, and can be used interchangeably. Although the most common form in writing is “Berglyd”, the official name of the farm is “Berrjod”. Signs in the area point to “Berglyd”, though the locals mostly say “Berrjod”. Its rarity in writing is probably also the reason that “Berrjod” is often misspelled “Berjo”.
Having said that, I personally much prefer “Berrjod”, for its authenticity.