Yes, WinXP stores your username twice ("Full name" and "User Name") and
Cygwin uses the "hidden" one ("User Name"), but I'm pretty sure you
don't have to reinstall XP to change it!
IIRC, you can change the username from Control Panel->User
Accounts->Advanced tab->Advanced button->Users->right click on the user
and select "Rename". You might need to be Administrator to do this,
though (and it only works for local users, so if you're on a domain, you
need to contact the domain admin).
Also, as someone already said, it is trivial to replace the
names-with-spaces in the /etc/passwd file with names that have no
spaces, as long as you don't mess with the SID.