I've heard two stories about the name rarebit or rabbit.
I doubt that they are true but they were interesting to me.
The first was due to the Welshmen's fondness for roasted cheese they referred to it as a rare bit of cheese later shortened to rarebit.
The second was a Welshman returned home from hunting empty-handed and his wife made him a rabbit out of cheese for his dinner.
Why there are no Welshmen in heaven
“I find written among old stories how God made Saint Peter port of Heaven, and how God, in his goodness soon after his suffering on the cross allowed many men to come to the kingdom of heaven who very little deserved it. So at this time there were in heaven a lot of Welshmen, who troubled all the rest with their boasting and chatter. So God said to Saint Peter that he was fed up with them, and that he’d be very glad to have them out of heaven. Saint Peter replied to him,
“Good lord, I guarantee that it will be done in no time.” So Saint Peter went outside the gates of heaven and shouted in a loud voice,
“Cause bobe!” which is as much as to say, “Roasted cheese.”
When they heard this the Welshmen ran out of heaven at great speed. And when Saint Peter saw that they were all outside, he quickly went in to Heaven and locked the door, and so he barred all the Welshmen out.
By this you can see that there is no sense in a man loving or setting his mind too much upon any dainty or worldly pleasure whereby he may lose heavenly or eternal joy.”