The relationship of 'goblin' to 'kobold' is a theory proposed by the Oxford English Dictionary, which suggests the following derivation (we've taken the liberty of expanding their standard abbreviations):
'Middle English, probably from Anglo-French *gobelin, medieval Latin gobelinus, probably from name diminutive of Gobel, related to Kobold'
The Concise Oxford Dictionary of Current English
In fact, there are at least two other theories. The first concerns two medieval parties, the Guelphs and the Ghibellines. The Guelphs were supposed to have despised their rival Ghibellines so much that their name became a 'bogey' word, and ultimately evolved into modern 'goblin'. The Ghibellines despised the Guelphs in equal measure, and so their name, too, apparently descended to modern times as 'elf'. Ingenious and economical as this theory is, it is almost certainly wrong.
A somewhat more plausible idea relates goblins back to the almost-forgotten fairy figure of Ghob, the King of the Gnomes. In Old English, the earth-spirits who followed him might well have been referred to as Ghoblings, and this gives us a third possible source of the name, somewhat older than the other two.