i'd recommend not using the two programs together - if you have to load up itunes make sure your ipod isn't plugged in. it's not that anything terrible happens, i've just had a bit of problem with it (itunes) scrambling the database (on the ipod) so i get incorrect cover art showing up when playing back (again on the ipod). the two applications seem to happily co-exist, it just seems to cause minor issues when they're both trying to control your ipod.
as to your question, i think the way MC works is that it takes the unique ID/Serial# of your ipod, then stores the name you enter in it's own database - so the name of your ipod never exists on the ipod itself, just in MC's own config/database. that's why itunes doesn't pick up on the name. i'm assuming this not just cos that seems the best way to do it - but because even if you do a restore of your ipod (which wipes everything), MC remembers the name of it.