For example, Dick is short for Richard but I never quite got why. What other common nicknames can you think of that have little or no resemblance to their longer counterpart?
Peggy for Margaret is the worst offender.
Sacha / Alexander
ETA: Or Sasha, I guess.
Sally for Sarah
Molly for Mary/Margaret
Babs = Barbara
Buffy = Elizabeth
Jack for John.
Even moreso, Peggy for Margaret.
Bob for Robert.
This one above all though, I’ve never understood. It’s not even shorter so WTF? 
“Jack” as a diminutive for “John” has always struck me as a bit odd. They only have one letter in common, and “Jack” isn’t any shorter.
On preview: Beaten to the punch by DCnDC, but the point stands.
Daisy for Margaret is worse, in my opinion.
Chuck for Charles (although they both start with Ch)
At that point, I think it just suggests that no one wants to be called (or say) “Margaret” more than necessary.
Never mind, beaten to it by Tripolar.
Nice. If I ever have a daughter, or alternatively, discover some manner of swamp monster, she’s totally getting named “Mog.”
Somehow I missed post 2. Sorry, what do I type here.
The Master has also discussed Dick, Bob, and Bill. The short version is that rhyming nicknames were once popular, and a few of them stuck.
Sadie is a nic for Sarah.
I had an Aunt Sadie
I don’t get Peggy from Margaret.
Now it’s also the diminutive for Mercedes.