Bear in mind that most recruiters and many in-house HR departments now use automated search tools and you can see the problem. Put "Red Hat" on your resume, and you'll be invisible to a recruiter looking for "Linux" using any of the more simple minded, and thus common, search tools.
So what can you do? Tailor your resume to text search engines that rely on simple word matches - mention every Unix variant you can reasonably claim at least once, but be prepared to justify your inclusions to a sceptical recruiter.
One resume I saw recently aced this. She had an introductory section summarizing her expertise in which she explicitly claimed hands on experience with Red Hat Linux, HP-UX, and SCO OpenServer -and pointed out that much of what she learned would apply to future work with other Unix products including Debian, Solaris, and NetBSD. Then she had supporting sections listing the employers and roles where she gained her experience and mentioned the lookalikes in each case -mentioning, for example, skill portability to Debian where she talked about the work she'd done using Red Hat.
Do a "quick Search" for a someone with Debian experience in a package like Staffsoft's and boom - she shows up twice even though she's never used Debian and didn't lie on her resume either.
There are some things you should remember about this strategy. First, don't waste time doing this in your covering letter, most agencies and HR departments throw those away before storing your resume.doc or scanning it in. More importantly, however, don't exaggerate: remember, your goal isn't just to get the recruiter to notice you, it's to get the recruiter to notice you positively. Most recruiters who don't know if technology A maps to technology B will ask a colleague or phone the employer to check acceptability. Win on that and you're golden, lose and you won't get a job there job no matter how often your resume pops up.