Help please
I looked up a dictionary for the meaning of
affectionately! Here there are the meaning and example of how to use this adverb:
Meaning:in a way that shows caring feelings and love for sb.
Example:William was affectionately known as Billy.
The thing I can't understand is that William is called Billy because he shows caring for other or others have a caring feelings twords William so that they call him Billy
( I know this is a silly question but I really want to know how this sentence is interrupted 😅)

Question

Help please
I looked up a dictionary for the meaning of 
affectionately! Here there are the meaning and example of how to use this adverb:
Meaning:in a way that shows caring feelings and love for sb.
Example:William was affectionately known as Billy.
The thing I can't understand is that William is called Billy because he shows caring for other or others have a caring feelings twords William so that they call him Billy
( I know this is a silly question but I really want to know how this sentence is interrupted 😅)

Answer

How this sentence is interpreted*

The people have affection for him, so they give him a nickname, Billy.

Answer

In English, many names are shortened to one syllable.  Susan becomes Sue.  William become Will.  A "y" is often added for children.  Susan becomes Suzy.  William becomes Willy.

Bill is a common alternative to Will/William.
Billy and Willy are common alternatives for children.

Usage examples:

His parents called him "Billy" unless they were angry, in which case they called him by his full name "William."

His friends called him "Billy," but the teachers called him "William."

Answer

"William is affectionately known as Billy" = "Friends of William who know him very well give him the nickname of Billy" ;)