Does the name Shiki have some sort of relevance to Death?
It is probably related to the fact that "shi" is death in Japanese. The kanji for death is "死", however, which does not appear in any of the names of characters you listed. The word would still be associated with death, (as shown by the tetraphobia that appears throughout Japan).

Those characters are all from Type-Moon series, also, so the connection may also come from that fact. Tsukihime and Melty Blood are directly related, existing in the same world, while Kara no Kyoukai is not.