I'm not sure. 4 and death just sound the same, it's more a superstition to avoid saying those numbers, like Westerners thinking 13 is unlucky. It doesn't extend to all words beginning with or containing "shi"

Also, shiro (城 castle or 白 white) is not the same as the name Shirō (e.g. 四郎 "fourth son", 志郎 "determined son"?, 史郎 "historical son"?)