The reason you couldn’t change the gid was because the number was already in use. I sidestepped that issue in my previous example by uninstalling the package that had appropriated the 1000 gid. In your case you would likely want to disable auto login if it is using 1000. You can re-enable auto login later and it will be given a higher gid.
You need to change the group ID that is currently 1000 to a higher number, then change your user’s gid to 1000 as in the example below:
@petsam may be correct in that having both the uid & gid identical may not be entirely essential. However, that is the way I always configure my system, and that is the way most installers configure a new system by default. I always setup all my systems with an account with the same username, uid and gid. This avoids access issues on drives formatted with a Linux file system that restricts the access permissions.
I assume it was setting up your system with auto login at install time that changed the default GID. I have experienced this on some distros, so I will only enable auto login after installation to avoid this. The standard gid & uid on most installs is usually 1000 for the first user account setup on the system.
Maybe @petsam is correct, as he is very knowledgable. I would chalk the friction between both of you up to the difficulty translating Greek to English, (as Greek is @petsam’s native tongue). Translations can often come off as more brusque than intended. Please don’t take such offense at someone’s comments, who is after all only trying to help you.