The title "On My First Son" is kind of vague. A title like this could be about almost any aspect of one's "first son." It could refer to the birth of the speaker's first son, or it could just be about how the speaker's first son flushed his car keys down the toilet. The point is, we have no idea that the poem is about the death of the little boy until we start reading it, and even when we start reading it we don't know right away that the son is dead. (The "Farewell" in line 1 could just be part of a story about the speaker saying goodbye to his son as he goes to school, or maybe to the fetch the plumber for those keys.)
The vagueness of the title does two things. First, it makes us want to keep reading—when we see a title like that we're curious. "What about this son?" we want to know. Second, and more importantly, it keeps the son "alive" for a brief period of time. By not calling the poem "On the Death of My First Son," the speaker is in some way able to pretend that his son is still living, or that the poem is about something else besides his son's death. This gives us a sense of really just how painful this loss is for the speaker.