A certain Albert Rachimi has successfully registered the trademark Ice Cube, despite opposition from Gilman S.p.A. who has word-marks Ice (TM69325) and Iceberg (69330) in the same category 25.
Apparently, not only is Ice Cube distinctive, but the word is considered sufficiently generic with regards to clothes that there is no dilution or assumed relationship.
I would asume that the word Ice for clothing is supposed to imply that the brand is “cool”. The word “cube” seems somewhat “square”. I have no idea what any of the various ice related brands look like.
One of Israel’s more popular brands of clothes, with shops in malls and on high streets, is Fox. There is a whole family of related brands: Fox Men, Fox Women, Fox Kids, Fox Babies, etc. One wonders if there is anything particularly different between Fox and Ice? Since Men, Women and Babies are obviously totally generic, could I open a shop called Fox Grandma? Fox Teenager? Fox Young Professional? Fox Yuppy?