In reply to:

But why is Randy in particular funny--more than, say, Dick?

UK Randy is an approximate (I was going to put rough but decided that was open to misinterpretation) equivalent to US horny, though randy implies, I think, a more permanent character than a temporary state like horny. Imagine innocent USn introducing himself in the UK, "Hi, I'm Randy". Grammatically it doesn't work so well with Dick because the double entendre would require "I'm a dick" rather than "I'm Dick". Also Dick is well known as a name in UK (Dick Turpin and all that) but Randy is only known as a name in a USn context.

Bingley


Bingley