Interestingly, in that lengthy prayer recorded in John 17, Jesus does not utter God's name a single time. One would expect that he'd at least be recorded as saying it on that occasion.
The Society also reasons that Jesus would not be afraid to use God's name around those who thought it blasphemous to utter it. However, the question isn't one of fear, but of simply going with the flow of the prevailing view of the time. The bottom line is that in the available written record we have (the Gospels and Acts 1) of Jesus' actual words, we do not find God's name being used, save for the possibility of the quote from Isaiah 61 at Luke 4. And even that is based mainly on supposition - i.e., 'the divine name was there in the Hebrew text, so Jesus likely used it'.