You could use the same approach as in this answer to your previous question, only use && in this case:
REG QUERY "whatever\you\want\to\query" >NUL && ECHO %COMPUTERNAME%>>C:\Log.txt
Similarly to FINDSTR, REG also sets ERRORLEVEL to a non-zero value if the search was unsuccessful, which allows us to use constructs with || and && as appropriate. The command after && is executed only if the search has been successful.
The above command suppresses standard output of REG with >NUL. If the search fails, the corresponding error message will still be displayed, because it is sent to the standard error device, rather than to the standard output. You can additionally suppress possible error messages by adding 2>NUL or like in @aphoria's answer.