$0can't be assigned in Dash. This becomes a command name.
$0 can not be changed in Dash.
You appear to be trying to assign a new value to
$0 in Dash.
Dash does not support this. Write around it, or switch to Bash.
If you instead wanted to compare the value of
$0, use a comparison like
[ "$0" = "myname" ].
ShellCheck is a static analysis tool for shell scripts. This page is part of its documentation.