Sofar, the Linux live session user is mint and $HOME is /home/mint. But in Linux mint21.3, the live session user is linux and $HOME is /home/linux, though it is mentioned as mint in the official website. I am confused. Where does the issue lies?

Which live version are you running i.e. Cinnamon, MATE or Xfce? The 21.3 Xfce live version default user is mint but I did not check the others.

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Thank you for your response. Now, I am completely perturbed. I have tried beta versions of Linux mint 21.3 cinnamon, Mate and xfce downloaded from https://ftp.heanet.ie/mirrors/linuxmint.com/testing/ and stable versions of Linux mint 21.3 cinnamon, Mate and xfce downloaded from official web site https://linuxmint.com/. In all three beta versions and three stable versions, the live session user is linux, shell prompt is linux@linux and home dir is /home/linux and $HOME is /home/linux. Also, there is neither mint live session user nor mint group. I am using Linux mint cinnamon live session since 2009. I have so many scripts with mint user and it is very difficult to shift my loyalty from mint login. I could not comprehend where do I go wrong. I need help.

I checked Cinnamon from a couple of different mirror sites, verified the checksum and the username was mint in both cases. I have no clue.

Well if you didn't report it during beta, not much chance of it getting changed now, even if it wasn't done for good reason. Guess you'll have to adapt your scripts or create the username you want.

The issue solved.
The issue lies in the grub.cfg file. Upto Linuxmint version21.2
linux (loop)/casper/vmlinuz boot=casper iso-scan/filename=$isofile noeject noprompt splash --
but from Linuxmint version21.3
linux /casper/vmlinuz boot=casper username=mint hostname=mint quiet splash --

ie. username=mint hostname=mint is added now which is not in previous versions:

After revising my grub.cfg file, the issue is solved.
Thanks everybody who have made suggestions and viewed. As the issue is solved the post is considered closed.