Comment there are 18 TMs "Adobe" by different companies (Score 1) 602
US PTO registered 103 Trademarks containing word Adobe, 18 of them consist of only one word:"Adobe" and only one of the latter is registered by Adobe we are talking about.
In 1997 adobe dropped trademark: "Adobe Type Set" :
ADOBE TYPE SET
Goods and Services (CANCELLED) IC 009. US 038. G & S: computer programs for creating fonts. FIRST USE: 19900221. FIRST USE IN COMMERCE: 19900221
Live/Dead Indicator DEAD
Cancellation Date October 13, 1997
I would suggest KIllustrator register it in its name and use as a part of KIllustrator Package
About registered trademarks containing word "Illustrator" and who owns them read my previous posting in this thread