Question: Jesus names the wrong man?
Mark 2:23-26 Jesus says Abiathar was the high priest and David was NOT alone.
1 Samuel 21:1-6 states that David met Ahimelech and David was ALONE.
Response: Actually both men were alive at that time. Abiathar was Ahimelech's son. Abiathar became the high priest after his father. Mark 2:23-26 is saying that this event in which David entered the House of God happened during the time of Abiathar, and that is correct. It did happen during the time of Abiathar. However, Abiathar was not yet the high priest. But the passage isn't necessarily claiming that he was the high priest at that point. Instead, the verse is identifying Abiathar as high priest, which is true, and it is saying that the event took place during Abiathar's time, which is also true. Imagine if someone said, "I knew President Bush when he was a student at Yale..." That person of course would not be claiming that Bush was actually president while still a student at Yale. No, he would only be identifying Bush as president and as a student at Yale. Nothing more, nothing less.
So why would Mark 2:23-26 speak of Abiathar instead of Ahimelech? Perhaps because Abiathar was better known. Abiathar shared a lot of adventures with David. The two are linked together in several Biblical accounts. And it is quite possible that many of the Rabbis during the time of Jesus held the memory of Abiathar in high regard, and Jesus would have known that.
As for the issue of whether David was alone - Mark 2:23-26 does NOT say that David's men entered the House of God with David. It only says that David himself entered. And it explains why he entered - because he and his men were hungry. But it never says anything about his men entering the House of God. It only says that David entered the House of God and got the bread, which he presumably later gave to his men. There is no conflict there.