How can I merge multiple PDF files with the same first 6 characters together, but in separate files?

I think this could be done very easily with a command-line utility such as CPDF (Coherent PDF) or QPDF. On a Mac at least, it would be simple to write a small Applescript that would contain the logic to call the command-line utility to do exactly what you want. Dunno how to call it in Windows. I've used CPDF quite a bit in the past, and it's very useful, but note that it is free only for personal use; any commercial use requires a license. Not sure about QPDF. Good luck!

How many files do you regularly proceed? Is it a one time job or a regular job to be done? For the later, tools like Enfocus Switch can be used to simply merge those PDF files using the dynamic digits as a reference key. 

If you want to do it with Acrobat you can, except for the last part. It can't delete files, only create new ones.

It would also require using an Action to open and then process ALL of these files, one by one, which might prove to be too much for it to handle. And it would require writing a custom-made script, of course.

Another option is to do it using a stand-alone tool, which is much more robust than Acrobat and can merge the files without actually opening them. It could also delete the originals, if that's what you wanted.

If you're interested in hiring a professional to create either tool for you, feel free to contact me privately by clicking my user-name and then on "Send a Message".