bash script names appearing in ps ax

[Joel Hammer]

I have noticed that with some bash scripts, the script
name appears when you run:
     ps ax
With other script names, only /bin/bash appears with ps ax.

For example, this script, named junk1.scr:

     ps ax | grep junk1.scr

returns nothing. 

But this script, named Master.scr:

     ps ax | grep Master.scr

returns the process Master.scr. 

This seems to be related to whether the first letter of the
script is a capital. Does anyone know if this is really
true? Is this a bug or a feature? Should this be relied
upon, or might this change in future versions of bash?

Thanks,

Joel