Project Euler 22: Names scores
Well, there's a potentially more efficient way:

Read the whole file into a byte-array (It's not even a measly 64K), thus avoiding any conversion overhead and most object-allocations, extract the start-indices of all the names, and sort them.

Is it equally nice? Probably not. And it will only speed it up by a constant factor, because more just isn't there to be had.
Anyway, measure it because while going down a level gives opportunities for optimization, it's easy to get it wrong.
If you don't want to go quite that far, here's an easy one: Strip the trailing " from the last name, and you can drop the test whether you actually have a letter in getValueOfName.
Getting to your constants name, that's atrocious. Because, you know, using a named constant for that at all is so bad.
You can simply use a character-literal: 'A'-1
You fail to close the file in readAllNames if newing the BufferedReader fails. Admittedly that's unlikely in such a small program, but anyway.
Also, why do you catch IOException there, but then return null which immediately causes a NPE in turn in main?