how to keep an offline database of my own games What would be the most standard way to keep an offline database of my online and over the board games?

Would just keeping PGN files (with arbitrary filenames) in a directory work? Would  database browser programs like Scid vs. Pc then be able to browse such a collection of files? or do I need other tools to generate a database out of a collection of PGN files? Is there a file-naming convention for the PGN files I have to be aware of?

The database browsing tool I use is Scid vs. Pc which I run in Ubuntu under wine but I am open to other suggestions as well.
PGN files is definitely the best way to go. PGN is an open and human readable format. Merging two PGN files is very easy; simply copy the content of one PGN file to the end of another. 

How you want to organize your PGN files is up to you. You may want to store your PGN files all in one directory, or you may want to store them in separate directories (based on tournament, opening, result, side, etc.) under the same root directory.  

ScidvsPc has the capability to browse through directories and select games you want to view. You can also manually browse the directories and double clicking the pgn will open the game directly in ScidvsPc (if you have set it up to work that way). 

There is no file naming convention for PGN files. You don't need any special tools to create a single database from PGN files. Since you're on Ububtu, you can use the capabilities of the Linux sed tool to merge files recursively under a root directory.