A name can tell you a lot about someone or something. A name can teach you history, culture, and characteristics of some person, a certain place or area, or anything in general. For example, the name of the city of San Francisco alone can teach us quite a bit.
San Francisco is Spanish for Saint Francis and is named after the Catholic Saint Francis of Assisi. The name teaches of San Francisco's history of being founded by Catholic priests from Spain who settled there in the 18th century.
Names of people can also give you historical insight of their genealogy. My mother's maiden name is Bunker.
My father's name actually has quite some meaning as well.
Just as my dad changed his name in order to follow Christ, we likewise promise to "take upon [ourselves] the name of Christ, by baptism" (2 Nephi 31:13). In other words, we promise to be Christians when we are baptized. To be a Christian is more than simply acknowledging that Jesus Christ was something special, but to represent Him and His teachings in all that we do. A follower of Christ will "bear one another’s burdens... mourn with those that mourn... comfort those that stand in need of comfort, and... stand as [a witness] of God at all times and in all things, and in all places that [they] may be in (Mosiah 18:8-9)."