I've it up in gunicorn.conf.py file as given here:

proc_name = "gunicorn"
default_proc_name = "gunicorn"

I referred the gunicorn docs https://docs.gunicorn.org/en/stable/settings.html

And run the service like:

gunicorn --name "gunicorn" -c gunicorn.conf.py wsgi:app

Even if you don't specify the --name flag, the default is set to be gunicorn.

and when the gunicorn service starts, it sets the values correctly and logs like: