Where can I find an exhaustive list of all of the names of Hashem (preferably שמות and כינוים) in Tanach and elsewhere?
Is this too ill-defined a topic to have an exhaustive answer?
Do the 70 in the midrash on Shir Hashirim count?
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Sepher Shorshei HaShemot by Rabbi Moshe Zecuto is an exhaustive listing of divine names. It is an alphabetical index. Each entry lists the source of the name as well as its usage.
In one of the Ba'al HaTurim's comments (available with English translation and commentary by Artscroll), he lists all of the names of Hashem.
As Alex writes in the comment, it is in the short commentary on Numbers 11:16, in parashat Behaalotecha. It is viewable here, starting two lines from the bottom.
Read this interesting article: תוכן הספר