AFAIK the answer to both is **No**.

The frame padding can be configured by adding `#` to the filename:

From the [wiki page on CLI rendering][1]:

>      -o or --render-output <path>
>          Set the render path and file name.
>          Use // at the start of the path to
>              render relative to the blend file.
>          The # characters are replaced by the frame number, and used to define zero padding.
>              ani_##_test.png becomes ani_01_test.png
>              test-######.png becomes test-000001.png
>              When the filename does not contain #, The suffix #### is added to the filename
>          The frame number will be added at the end of the filename.
>              eg: blender -b foobar.blend -o //render_ -F PNG -x 1 -a
>              //render_ becomes //render_####, writing frames as //render_0001.png//

This works in the GUI too:

 ![enter image description here][2]

Becomes `render01.png`, `render02.png` etc.

One `#` = no padding. (i.e. `render1.png`)

I don't think there is a way to remove the frame number completely from blender, though it's really not hard to remove it later.



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  [1]: http://wiki.blender.org/index.php/Doc:2.6/Manual/Render/Command_Line
  [2]: https://i.sstatic.net/dAcFn.png