Deathberry is a nickname Kubo Tite sometimes uses to refer to Ichigo in chapter titles. It's probably the combination of words that describe parts of Ichigo's character. The word "death" comes from death god, since he is after all a shinigami representative. And "berry" comes from strawberry. Although his name is written with the characters ichi ( 一 ) as in "one" and go ( 護 ) from "guardian", his name meaning "one who protects", it's pronounced the same way as イチゴ, the Japanese word for "strawberry" (a fact he is sometimes teased about). On a related tangent, "ichigo" can also mean 'one' and 'five' if the "go" is written as 五. That's why he has a sign that says "15" on his bedroom door, and he sometimes wears shirts with the number 15.
As with the nickname Deathberry, this shot was meant to depict two sides of his identity - the seemingly regular teenage boy (whom Kubo Tite sometimes dresses in the craziest outfits in his illustrations) with hair as striking as his personality, and the Hollow he struggles to suppress inside him.