The custom is to transliterate foreign words and names into Katakana, but due to the sound-poor nature of the Japanese syllabary, you will get something to the extent of "GU RI — GU". The exclamation point is recognized but not standard Japanese punctuation. You can use it, but I don't think it can be incorporated a sone of the letters. I could be mistaken, as I'm out of practice with Katakana.

It might be simplest to keep the existing logo and simply add the katakana reading (グリーグ) in smaller type. Perhaps above the name, to balance the 2007. The combination of Latin logo with subsidiary Japanese reading seems to be fairly common in Japanese design.

(The exclamation mark is perfectly standard punctuation in modern Japanese, but there isn't an obvious place to incorporate it in the kana. I doubt they want the logo completely redone in Japanese, though.)

I second Haeleth's comment. Inserting the katakana would probably be enough, so that people would know how to pronounce it.

Perhaps something like the attachment.