Why do some nicknames have no apparent relation with their original counterparts? [duplicate]

I find it unusual and rather contrary to common sense and logic that some nicknames should have no apparent relation to their original names, such as "Jack" for "John(eg. JFK)" or "Jonathan", "Patsy" for "Martha," or "Ted" for "Edward"(shouldn't it be Ed or Eddie?).

"Bill" for "William"(if someone could explain this to me, it would be great), "Jim or Jimmy" for "James" are still understandable as they rhyme in some degree with the pronunciation of the originals.

I wonder how this happened and why should the resulting tradition still be in use in today's English.

Can anyone enlighten me ?

There is no clear origin for such nicknames:

BILL from WILLIAM:

• There are many theories on why Bill became a nickname for William; the most obvious is that it was part of the Middle Ages trend of letter swapping. Much how Dick is a rhyming nickname for Rick, the same is true of Bill and Will. Because hard consonants are easier to pronounce than soft ones, some believe Will morphed into Bill for phonetic reasons. Interestingly, when William III ruled over in England in the late 17th century, his subjects mockingly referred to him as "King Billy."

JACK from JOHN:

• The name Jack dates back to about 1,200 and was originally used as a generic name for peasants. Over time, Jack worked his way into words such as lumberjack and steeplejack. Even jackass, the commonly used term for a donkey, retains its generic essence in the word Jack. Of course, John was once used as a generic name for English commoners and peasants, (John Doe) which could be why Jack came became his nickname. But the more likely explanation is that Normans added -kin when they wanted to make a diminutive. And Jen was their way of saying John. So little John became Jenkin and time turned that into Jakin, which ultimately became Jack.

TED from EDWARD:

• The name Ted is yet another result of the Old English tradition of letter swapping. Since there were a limited number of first names in the Middle Ages, letter swapping allowed people to differentiate between people with the same name. It was common to replace the first letter of a name that began with a vowel, as in Edward, with an easier to pronounce consonant, such as T. Of course, Ted was already a popular nickname for Theodore, which makes it one of the only nicknames derived from two different first names.

PEGGY from MARGARET:

• The name Margaret has a variety of different nicknames. Some are obvious, as in Meg, Mog and Maggie, while others are downright strange, like Daisy. But it's the Mog/Meg we want to concentrate on here as those nicknames later morphed into the rhymed forms Pog(gy) and Peg(gy).

(source: mentalfloss.com)

While @Josh's answer is good and provides quite a lot of historical background for some of the specific nicknames, it doesn't completely address why, in general, names are truncated: the nicknames you've listed are diminutives:

A diminutive is a word which has been modified to convey a slighter degree of its root meaning, to convey the smallness of the object or quality named, or to convey a sense of intimacy or endearment...they are often employed as nicknames and pet names.

There's a link in that particular Wikipedia article for diminutives by language. Under that subsequent article, there are several names under the English subheading which are along the lines of the names you've listed:

The most common include shortening a longer name (e.g., "Pete" for Peter) or adding the diminutive suffix /i/ ("movie" for moving picture), variously spelled -y ("Sally" for Sarah), -ie ("Maggie" for Margaret), and -i ("Dani" for Danielle).

In short, such nicknames don't have to make sense based on the spelling of the original word (e.g. "Bill" for "William"); they're more commonly based on sound and length, as well as the "friendliness" of the alternative nickname form. In this case, "Bill" is much more informal, casual, and friendly than "William". In an exaggerated sense, think of it as the difference between your good friend "Bill" from the office and some nobleman named "William" from, say, England.