The name "Bleach" seems to be having no relevance to the plot unlike most other series. Was it just chosen at Kubo-sensei's whim or does it have some significance? Maybe some cultural significance associated with shinigami, etc. that I am now aware of?
Kubo himself has commented on this. Below I've taken the quote from Bleach Answers Wiki:
The title wasn't Bleach when Tite Kubo decided to draw a story about Shinigami. This was before he drew the one-shot manga that appeared in Akamaru Jump. The weapon wasn't a sword, but a scythe. Only Rukia had a scythe and the other characters used guns. At that point, the title was Snipe (as in "Sniper"). Right before he started drawing, he began to think that a sword would be better and realized he couldn't use Snipe as a title anymore. He began looking for a title that grasped the bigger picture. Shinigami are associated with the color black, but it would have been boring to use "black". "White", on the other hand, can suggest black as a complementary color. So Tite Kubo chose "Bleach" to evoke the impression of the color white.
I've also heard other theories, which aren't as well supported by interviews with Kubo but still seem to have some evidence supporting them. One is that shinigami "cleanse" souls, similar to what bleach does (Kubo himself mentioned this in an interview, but it's not clear whether he noticed this before or after deciding on the name). Another is that Kubo is a fan of the band Nirvana, and their first album is Bleach. So there might be more than one reason, but the quoted one above is the one he usually gives when asked about it.
According to the creator, Tite Kubo, when the Shinigami strike a Hollow with their Zanpaktou, they bleach (i.e. clean) the darkness and evil in the Hollows.
Or maybe Ichigo is bleaching his hair to that color so it would be closer to a version he remembers his mother having? And the title is about him - who is the main character, after all?