I cannot find a way to build a custom name without it inserting an underscore between the two parts. I use a ten digit system witht the last four as the sequence number. If I put it all in the first custom tab it won't increase by 1. If I add a sequence group it inserts an underscore which I then have to delete by hand. It really defeats the whole purpose of setting up a file name if I cannot do what I want. It is just numbers. I shoot an original 5D, raw, srgb. My numbering system predates digital photography so it is too late to design a new protocol.
What difference does it make? You're shooting RAW, so you'll have a post-processing step; and any decent photo editor will let you rename the files to suit your naming scheme. You need to be concerned about how the camera names the files only if you're shooting with multiple cameras and want to keep track of which images came from which camera. And even then, you'll probably change the names in PP.
There are relatively limited in-camera file naming choices, if that's what you were hoping for.
One relatively simple solution is FastStone Image Resizer, which can do many different batch processes to images after downloading them, inluding renaming them as you see fit. It's freeware and is available here.
I used to use Faststone... but now use Adobe Lightroom, which has powerful and highly customizable file renaming capabilities too. I renamed over 3000 photos taken last Sunday with it in a few minutes.
I think most image cataloging/editing softwares have some sort of batch naming feature.
I did try lightroom I didn't think it solved the main issue "underscores" all systems seem to want that. But I will check it again, maybe I missed it or didn't experiment enough.
Definitely experiment some more with the custom file naming features of LR, since it sounds as if you already have and use it.
In some of the default naming schemes it adds underscores as spacers. But you don't have to use those at all if you set up your own custom naming conventions.
Look at the pull down menu for file naming... all the way at the bottom is "edit" and that's what you want. Study some of the other naming commands (such as sequence, dates, etc.) if you want to use those.
Lightroom should be able to do that on import with a preset. Automatically, without any input from you. I don't do renaming on import because I use LR Collections and rename there. But it sounds like that is a basic LR feature. Try LR 6, it is free for 30 days.