The NT spiritual use of life can either refer to the new life of regeneration (which precedes salvation) OR eternal life which comes with salvation. In other words, God gives us new life (regeneration) so we can have eternal life (justification). Traditional reformed theology doesn't equate regeneration to justification. So a Calvinist would read the verse as saying "so that having faith you may have ETERNAL life in His name."
Yes, I understand that Calvinists must apply custom definitions to plain scripture in order for their theology to work for them. I also understand, according to Calvinism, that free will to come to Christ is something you get from God if He determines you should have it.