I know this is a month old, but I'm going to weigh in anyway.
I discovered Linux Mint is a magazine article a few weeks ago. I never questioned the name, it sounded fine to me. Since then I have thrown it into conversation several times, and it's not a bad sounding combination of words, to me at least. To be honest, I struggled more with saying 'Ubuntu'. (Bless you).
Furthermore, I think having 'Linux' in there helps understanding of the OS. Linux is a strength! Maybe the word cold be de-emphasised somewhat in a revised logo, but it could be worse... Richard Stallman would insist on 'GNU/Linux Mint'!
So I wouldn't sweat it. Although the kerning could use a little polish. And what's with the shoulder on the second 'n'?...