Bash的exec命令有一个-a NAME选项：

nohup bash -c 'exec -a xxx sleep 12345'

根据help exec：

exec: exec [-cl] [-a name] [command [argument ...]] [redirection ...]
    Replace the shell with the given command.

    Execute COMMAND, replacing this shell with the specified program.
    ARGUMENTS become the arguments to COMMAND.  If COMMAND is not specified,
    any redirections take effect in the current shell.

    Options:
      -a name   pass NAME as the zeroth argument to COMMAND
      -c        execute COMMAND with an empty environment
      -l        place a dash in the zeroth argument to COMMAND

    If the command cannot be executed, a non-interactive shell exits, unless
    the shell option `execfail' is set.

    Exit Status:
    Returns success unless COMMAND is not found or a redirection error occurs.

首先，您不需要nohup;它可以做shell自己做不到的事情。

exec -a MyName1 MyCommand param1 >nohup.out 2>&1 </dev/null & disown -h "$!"
exec -a MyName2 MyCommand param2 >nohup.out 2>&1 </dev/null & disown -h "$!"

nohup所做的大部分工作只是重定向，其余部分与disown -h相同（它告诉shell不要将HUP信号转发给那个进程）。
当然，您也可以选择一个不同的文件来存储每个命令的日志，并将PID存储在变量中--执行后一种操作将完全避免使用pgrep。