A few notes about this band:
Rinne (凛廻) was the vocalist of a band called Vertige, and AI (アイ) and Haruna (遥那) are said to have been members of a band called Ver:tige.
Vertige has one known band photo, and two of the members are almost certainly AI (アイ) and Haruna (遥那), so I'm 90% sure that “Vertige” and “Ver:tige” are the same band. (I've arbitrarily assumed the latter is the correct name.)
In that same photograph, there is a fourth member, but I'm not sure who he is.
Also, the homepage of vocalist Rinne (凛廻) redirects to the Clothoid÷Doll website. Furthermore, the central figure in the Vertige photograph looks very similar to Clothoid÷Doll guitarist Aya (綺). So I believe, but can't confirm, that Rinne and Aya are the same person.
V. Rinne (凛廻) / G. AI (アイ) / B. Haruna (遥那) / (?)