Many have said that the selection of the name of a Pope is in conjunction with the preceeding Pope who had that name and that the new Pope will hold to many of his teachings. The only thing I can find for sure about Pope Benedict XV was that he was a great arbiter of peace during World War I and referred to all sides of the conflict as beligerants.
I was watching ABC news commentary at the time they were waiting for the Pope to appear. Fr. Richard McBrien was filling time and expounding what it would mean if the new Pope chose the name Benedict XVI.
He was saying how Benedict XV was known for an encyclical about bringing all factions of the Church together, specifically, conservatives, traditionalists, liberals, and progressives.
Our new Pope undoubtedly gave this name much thought beforehand, and will be a uniter.
BTW, McBrien was flabbergasted when he discovered Ratzinger ad been chosen, and again when he found out he had taken the name Benedict. He called it all "very controversial" which is lib speak for how could they elect this jerk.
God Bless and keep safe His Holiness Pope Benedict XVI