I'd like to install a new linux system using for i.e: liveCD or USB boot.
But at the time of install new system I'd like to change the name
Is there any way? Thanks in advance.
Since you seem not to be familiar with the system you're trying to install, it would be worth discussing this with a colleague who does understand it.
Alternatively use the installation defaults and amend them immediately afterwards. Here is one way to move the initial user's home directory, assuming that the user is called
usermod --home /user/user1 --move-home user1
You can also change the default value for future user accounts:
useradd --defaults --base-dir /user