There are a few pieces of image file renaming software available free on the internet. I used some a few years back (but cannot recall which) but in any event here are a couple you may wish to look at immediately below. My need at the time was similar to yours so I think you will find something..............
(The description of this one sounds to be close to what you want which says:
This mass file renamer is a great utility for organising digital pictures for both professionals and beginners. The thumbnail mode lets you display thumbnails directly in the file list giving you maximum control of the renaming process. With this program you can rename all your photos in a snap."
And this review gives some leads:
and this list of 50+ utilities does likewise:
Another bit of software I use a lot is (free) Faststone Image Viewer
. I find it good for creating slide shows (and even saving "movies" created from sets of image files complete with transitions / sound tracks etc) but cannot immediately recall if you can do a bulk file rename within it.
EDIT- I just had a closer look at Faststone. If you open a folder of unsorted image files in Faststone, and then right-click
on any one of these image files you can select an option Tools/Batch Rename i
n the popup menu.This brings up a window that allows you to view the files (in the left hand window) and then select them to move to the right hand half of the window (which is the input list for the renaming utility). You can order these files in that list based on the order in which you select them - but it seems not to allow you to then move them about / up and down in the input list once you have selected them. I have not tried but it seems that when you run your rename command it can rename them sequentially according to their order in that input list. Which I think is what you want). This looks reasonably simple but is not all that flexible given it relies upon the order of selection of the files to produce the naming sequence.