posted:

In the window that opens when you click Options, headed "Batch rename
settings", click Help. Scroll down. You will see $S - file size, and $m
- number of megapixels. So close the help, and change whatever's in the
"Name pattern" box to $S. Now select your files, and start renaming ...

This is IV 4.51, but I think it's been the same for a while.

I only later understood what you are trying to tell me.
Let me write what happens with IV 4.5.1 - 32 bit as I try slowly.

I open up a directory of a few thousand images of various types.
I only want to rename the base file name and keep original extensions.
I do not want the current order of the file names which is alphabetical.
I want the order of file names to be random (or at least mostly random).

I click twice on a file to open it up in iv which is my default pic viewer.
I press the "b" keyboard key to begin batch mode.
The "Batch conversion" window opens up.
I press the "Add all" button to add all the thousands of image files.

Under the heading of "Batch rename settings" is a "Name pattern".
To the right of that name pattern is an "Options" button.
I click that Options button which has a "Name pattern" again.
To the right of the "$N" and "#" example is a "Help" button.
I press that "Help" button which brings up "Text/Pattern Options" help.
Some of those text pattern options are below.
$S - file size
$m - number of megapixels
$B - image bits per pixel
$p - image DPI
$R - image aspect ratio (width / height)
$I - all IPTC data

Closing that Help I try this pattern
Name pattern: $S$m$B$p$R$I###
And then I press the "Start Batch" button.

That gives me random file names of
497.88 KB1.19 MP2496(0.87)001.jpg
473.31 KB1.12 MP2496(1.65)002.jpg
810.52 KB2.35 MP2496(0.95)003.jpg
608.40 KB1.81 MP2496(1.24)004.jpg
487.22 KB1.32 MP2496(1.94)005.jpg
1023.52 KB1.97 MP2496(1.14)006.jpg
924.00 KB2.12 MP2496(0.49)007.jpg
407.16 KB0.61 MP2496(1.72)008.jpg
591.69 KB0.93 MP2496(1.12)009.jpg
417.45 KB0.78 MP2496(1.34)010.jpg
259.61 KB0.44 MP2496(2.37)011.jpg
449.83 KB0.99 MP2496(1.05)012.jpg
591.44 KB0.96 MP24300(1.09)013.jpg
558.63 KB0.98 MP2496(1.07)014.jpg
569.74 KB1.13 MP2496(0.92)015.jpg

Now that the file name order is random, I can run another batch rename
Name pattern: image###

Now the images are in a pseudo random order.
It works ok.
Thank you for helping me find the other randomizing values!