Samuel's Explanation
Bible says that, God called Samuel three times - 1.Now the boy Samuel was ministering to the Lord in the presence of Eli. And the word of the Lord was rare in those days; there was no frequent vision. 2.At that time Eli, whose eyesight had begun to grow dim so that he could not see, was lying down in his own place. 3.The lamp of God had not yet gone out, and Samuel was lying down in the temple of the Lord, where the ark of God was. 4.Then the Lord called Samuel, and he said, Here I am! 5.and ran to Eli and said, Here I am, for you called me. But he said, I did not call; lie down again. So he went and lay down. 6.And the Lord called again, Samuel! and Samuel arose and went to Eli and said, Here I am, for you called me. But he said, I did not call, my son; lie down again. 7.Now Samuel did not yet know the Lord, and the word of the Lord had not yet been revealed to him. 8.And the Lord called Samuel again the third time, And he arose and went to Eli and said, Here I am, for you called me. Then Eli perceived that the Lord was calling the boy - 1 Samuel 3:3-8
but there is a slight difference every time the way God called Samuel, because our God is a Trinity God(Father, Word, and the Holy Spirit), and called Samuel separately.
That was the reason, when Samuel could not recognize God's second calling, the Bible says that the WORD of the Lord had not yet been revealed to Samuel.
And Eli must aware of the Trinity of our God, that why when Samuel went to him for third time, Eli could perceive that Lord is calling him.
And finally, the Lord Jesus Christ himself came to Samuel, and revealed the things that are yet to come - 9.Therefore Eli said to Samuel, Go, lie down, and if he calls you, you shall say, Speak, Lord, for your servant hears. So Samuel went and lay down in his place. 10.And the Lord came and stood, calling as at other times, Samuel! Samuel! And Samuel said, Speak, for your servant hears. 11.Then the Lord said to Samuel, Behold, I am about to do a thing in Israel at which the two ears of everyone who hears it will tingle - 1 Samuel 3:9-11
Samuel Means
The name Samuel means "His name is El" or "Name of God", so when God called Samuel three times, actually they were proclaiming Son Jesus Christ who is the image of Trinity God, and what Lord said its primarily about his suffering on the Cross for our salvation - 10.And the Lord came and stood, calling as at other times, Samuel! Samuel! And Samuel said, Speak, for your servant hears. 11.Then the Lord said to Samuel, Behold, I am about to do a thing in Israel at which the two ears of everyone who hears it will tingle - 1 Samuel 3:10-11
My Son
When God called Samuel three times, God also revealing the Trinity of Jesus Christ, so the name Samuel is the picture of Son Jesus Christ, that was the reason when Eli called "Samuel, My Son" Samuel responded "Here I AM" - 15.Samuel lay until morning; then he opened the doors of the house of the Lord. And Samuel was afraid to tell the vision to Eli. 16.But Eli called Samuel and said, Samuel, my son. And he said, Here I am - 1 Samuel 3:15-16
Opened the Door
Since Samuel picturing the Son Jesus Christ, his action also revealed what Christ is going to do on the Cross - he opened the doors of the house of the Lord - 1 Samuel 3:15b