Jhin's gun is named Whisper. This is more than 4 letters.

Ah, but if you knew the true nature of the name, you would instantly see why Jhin picked it. Going by the numbers corresponding to the order each letter appears in the alphabet, we get the following...

W=23, H=8, I=9, S=19, P=16, E=5, R=18

You may be thinking, there are still no fours to be seen, right? If you don't see it yet, I can't blame you. Jhin is a twisted genius after all. Now we must add the digits of each number together until each becomes a beautiful single digit.

2+3=5 8 9 1+9=10 -> 1+0=1 1+6=7 5 1+8=9

Now once we add all of these together, what number do we get? That's right, 44. Not only does Whisper truly contain Jhin's favorite number, it does so twice.

Whisper is a perfect name, I rest my case.

A shorter 4-letter name for "Whisper"?

Here you go:

http://dragonballsuper.info/wp-content/uploads/2016/08/Whis-3.png