You can't - as far as I know home is only called homeHow to I set the home directory name at install time?
You have to use different user names
Never ever use the same user name and home in more than one distro
One way to do this is not to have home on a separate partition in Mint and mount the home partition of the other distro in Mint's home
Something like the suggestion for a data partition here:
http://www.linuxmint.com/wiki/index.php ... _partition
In this case it is possible to use the same user name in both distros