A further quote from Manuals of Style, this time from the section which directly addresses the issue of mixed or non-capitalised.
"For trademarks that are given in mixed or non-capitalization by their owners (such as adidas), follow standard English text formatting and capitalization rules. ... The mixed or non-capitalized formatting should be mentioned in the article lead, or illustrated with a graphical logo."
Standard English text formatting and capitalisation rules would render GReeeeN as Greeeen, plain and simple. It's not even possible to use CamelCase as a defence, as it's capitalisation for capitalisations' sake within a single word. I'm not quite sure how much clearer I can make this.