il problema è lo stesso per tutti e due i casi.
Va configurato apache in modo che risponda, oltre che a localhost, anche al nome del tuo computer.
Questo, se ricordo bene, va settato nel file di configurazione di apache (httpd.conf). Vai a cercare il parametro servername...ecco quello che c'è scritto:

#
# ServerName allows you to set a host name which is sent back to clients for
# your server if it's different than the one the program would get (i.e., use
# "www" instead of the host's real name).
#
# Note: You cannot just invent host names and hope they work. The name you
# define here must be a valid DNS name for your host. If you don't understand
# this, ask your network administrator.
# If your host doesn't have a registered DNS name, enter its IP address here.
# You will have to access it by its address (e.g., http://123.45.67.89/)
# anyway, and this will make redirections work in a sensible way.
#
# 127.0.0.1 is the TCP/IP local loop-back address, often named localhost. Your
# machine always knows itself by this address. If you use Apache strictly for
# local testing and development, you may use 127.0.0.1 as the server name.
#
ServerName nomedeltuopc

La parte in grassetto è quella che devi settare...

Comunque secondo me ti conviene mantenere le parti separate piuttosto che passare easyPHP