Once you have inserted an image between your sequence, you can select those set of images and rename them again as custom so that your sequence is maintained and that image is included in your set.
Renaming them again can be done via the same process as you do for the first time by selecting the set of images > press F2 or go to Library menu > choose Rename Photos.
I have done that. But 2007_540_image2345677 then becomes 2007_541_2007_540_image2345677 because LR dos not "know" what portion of the old filename to keep to make it 2007_541_image2345677
Thanks for the update.
In that case, you need to create a new custom preset for filename and choose the following parameters to be included in the file name :
Date (YYYY) _ Sequence _ Original filename
Original filename would retrieve the "image2345677" portion and not the year and sequence set earlier.
Hope this would help.