Did you notice how frequently Jesus (in this prayer) mentioned the name of God? Three times, He did. The name represents what Jesus Christ is revealing to us about God. This is how you come to know God - through what Jesus Christ has revealed about God. We are kept by that name: First, by trusting in it as David did, as in Psalm 18. When David was in trouble, when he had need, he went to God, and he named names of God that would indicate what God would do for him.
And so we will be kept - we will be guarded; we will be preserved - by God because we know Him through the revelation of His name. But it also implies by obedience because of those names. Because we understand what those names mean, we are obedient to their nature - to their character - because they are showing what we ought to be following.
That is why Jesus said, Keep them through Your name. Those who know the name of God will put their trust in His name. They will have faith in it, and salvation is by grace through faith.