The names that Toni Morrison gives to her characters always carry more meaning than originally meets the eye. Beloved's name is explained as what's engraved on her tombstone. In the beginning of the novel we are told that Sethe could only remember the phrase "Dearly beloved" from the speech the preacher gave at the burial for the crawling already baby. Sethe thought the engraving was fitting because that's the most important thing about the baby -- that she was loved.
This explanation carries a lot more weight when we learn the full story of what happened to the baby girl. Sethe was the one that killed her, but she claims to have done it out of love. The name "Beloved" is an explanation and a justification for Sethe's actions.
The name also shows that Sethe is willing to do literally anything for her children. From traveling long distances to ensure they are fed, to killing them if it means they are spared the horrors of slavery. The story of how the engraving came about is another example of Sethe's fierce love. She pays the engraver in sexual favors to ensure that her daughter has something written on her tombstone. Sethe's motherly love is her defining characteristic and all of her actions are driven by her love. Again and again Sethe commits undeniably dauntless acts for her children, although some of them are morally questionable. Paul D tells her that her love is "too thick".
The full phrase from the funeral was probably something like "Dearly beloved: we are gathered today to pay our final tribute to...". "Dearly beloved" is what the preacher uses to address the congregation. The congregation is the "dearly beloved" of the deceased. In this case, since it was a baby, it would be all those who dearly loved the baby. Beloved is actually named after everyone who attended her funeral. Sethe misunderstood the preacher and thought he was referring to the baby. I sure that this misunderstanding is an intentional detail from Toni Morrison.
Beloved is named after all of the people of the town, who are both responsible for her arrival into freedom and the reason she died. The Underground Railroad system brought the baby to Cincinnati but also refused to warn Sethe that the four horsemen were approaching, leading to her desperate actions. Fitting the recurring theme in the novel, it's possible that the past lives in Beloved's present even through her name.
