It may be seen as different names if you take into acount adobe and GNU.
like MS office and open office.
But I have to admit that office is for office suit, and flex doesn't mean anything I'm aware of, perhaps cause I'm not native english speaker?

In the UK, it seems to be acceptable to use the same name as another company as long as you're making an entirely different product.

Adobe Flex and GNU Flex may both be software, but they're not related in any other way.

It'll make it more difficult to find useful information on either when searching by name, though.

Btw., it is not GNU Flex, but just Flex

Really, besides foxes aren't birds I'm happy I can google for Firebird the database server stuff and don't need to worry about avoiding Firebird the browser results.
I'm not sure how much searches people do for (f)lex resources, but this also can complicate things a bit for them.

I'm planning to move to the UK and release some software called Windows. It will be a completely different product, but it will still be an OS. :-D