While you can't change which designname file your empire looks for once the game has started, you can certainly edit the file itself; the new information in the file will be read when you try to name a new ship design (and if you delete the file, or never create it in the first place, the game will just complain that it can't find the appropriate file).
In other words, say you use "composers.txt" for your design name file. If, after playing the first few turns (or few hundred turns
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), you decide you need more names, just edit "composers.txt" to add more names. The new names will be available.
A more complicated scenario is when you would prefer to use a completely different set of names. Let's say you selected Romania.txt as your design name file at setup. Now, you want to use a custom file. You would copy the contents of the custom file, paste into the Romania.txt file, and probably delete all the old names in Romania.txt.
NOTE: This will affect all empires that use that design name file! I would also recommend, as usual, that you save a copy of the original file (I usually use the "backup" folder so thoughtfully provided in the SE4 folder).