In the Memories in the Rain chapters (17 to 19), the text states it outright: Masaki named her son with the kanji ichi and go, one and protect, a wish that he would protect the one thing that matters to him. The jokes are equally documented: ichigo is also the word for strawberry, which the series mines from chapter 1, and ichi-go reads as the numbers one and five, fifteen, the age he is when the story opens and the number on his door. Kubo's design notes confirm names are assigned with their roles attached: characters first, he insists in every interview, and the names come with the job description.
Fans long ago mapped the pattern: Ichigo is strawberry, his sisters Karin and Yuzu are written with other characters but homophonous with quince and citron, and the men's names (father Isshin, one-heart; son Kazui, one-brave) all carry the kanji for one. The family tree is a naming system, not a set of names.
The sharper reading: Ichigo's refusal in chapter 2, when Rukia tells him a protector of souls must protect all souls and he answers that he refuses the large responsibility but will not watch anyone suffer, is the name arguing with itself. One-protect, not all-protect. Critics of the series' ending note that the story closes with the name fulfilled at its smallest possible scope, one family, one town, one promise.
A name can be a blessing, a joke, and a plot summary at once. If your own name hid a mission statement, would you want to read it?