Just wanted to give the meaning of the word "bhagavan". The word contains "bhaga", which means qualities. A reality that has certain qualities or bhaga is called bhagavan. These qualities are six. This is mentioned by Adi Sankara in his introduction to his Bhagavad Gita commentary:
"He, the Lord, ever endowed with Knowledge, Sovereignty, Power, Strength, Valour, and Formidability..." In sanksrit, Jnanam, Aishwaryam, Vairagyam, Viryam, Yashas and Shree", these six qualities in their limitless form are called Bhaga. The one who has them is Bhagavan.
Aishwaryam - God can keep on giving us everything we want and still He doesn't become poor. He is All Wealth.
Jnanam - God is all-knowing. There is nothing in this universe, known and unknown to us, that is unknown by God. He is the Knowledge we seek.
Vairagyam - After eating a banana what is your disposition with reference to the banana peel? That is called "Vairagyam". It is this vairagyam that propels us towards Him. It is this vairagyam in God that makes Him an impartial judge.
Viryam - God has all the strength in limitless amount. He has the power to create, sustain and destroy. That is why this is a bhaga and that is why a reality with this bhaga is called a bhagavan.
Yashas - Simply means glory. It is because of HIS glory, that we live this existence. He is full of glory. There are no words to describe Him and praise Him.
Shree - Basically means prosperous. God never gets tired of always giving and never goes broke. He is the sustainer.
So basically, we can see these 6 qualities in all our Hindu mythological Gods like Murugan, Shiva, Vishnu, Ganesha, Durga, Krishna, Saraswati, Lakshmi, etc.
In the context of the Gita, Krishna too had all these 6 qualities. He had aishwaryam (he was a king), he was all-knowing (he had the knowledge of God that is as good as knowing everything), he had yashas (everybody praised Krishna), he had viryam (he had powerful knowledge of weapons as a kshatriya), he had shree (he was prosperous in every aspect of his life) and he also had vairagyam (without vairagyam or dispassion, one can never know God, so obviously Krishna had vairagyam).