In the poem's opening, the speaker uses apostrophe to address an unidentified group. Because of the use of the word "we" in the opening line ("Today we have naming of parts"), readers understand right away that this group also includes the speaker.
Going on, the speaker asserts in line 3 that there will be a lecture the following day about "what to do after firing"—a statement that, along with the use of the word "we," indicates that the speaker is addressing a group of soldiers and, more generally, that the speaker is (like the soldiers) in the military too. In this way, the use of apostrophe in the opening stanza helps readers put together the poem's overall setting, making it easy to infer that the speaker is a military official giving a lecture about weaponry to a group of new soldiers.
More specifically, the references to "daily cleaning" and "what to do after firing" suggest that the speaker will be teaching the soldiers about their military-issued rifles. At this point, the soldiers have already learned how to clean their guns, and now they will learn the technical names of the various parts.
It's worth noting that the speaker repeats the phrase, "Today we have naming of parts" in lines 1 and 4. This repetition instills a sense of order in the poem, and this ultimately reflects the militaristic environment and the speaker's commitment to procedure. This persistent desire to focus closely on the technical aspects of handling a weapon is also a way for the speaker to put off considering the broader implications of using a gun during wartime. After all, a military rifle lesson carries obviously violent connotations, since teaching soldiers about their weapons is a stepping stone toward teaching them how to use these weapons, which in turn is a stepping stone toward killing enemies.
In keeping with this, the speaker says, "And tomorrow morning, / We shall have what to do after firing. But to-day, / Today we have naming of parts." By saying this, the speaker acknowledges that the soldiers will eventually have to come to terms with the idea of actually firing their weapons. Even if the speaker is only thinking about this in technical terms (perhaps suggesting that the soldiers will have to do certain maintenance-related things after shooting their rifles), it's clear that these lines contain a recognition of the fact that there's more to being a soldier than simply naming the parts of a rifle.
However, the speaker is intent on focusing exclusively on this naming process, as evidenced by the repetition in lines 3 and 4: "But to-day," the speaker says after briefly mentioning the act of actually shooting the rifles, "Today we have naming of parts." By repeating the word "today," the speaker implies a desire to only think about the present, not wanting to consider the harsh realities of war, which will require the soldiers to use the rifles for violence. Instead of dwelling on this, the speaker becomes preoccupied with the mundane practice of cataloging the different rifle parts, effectively approaching the weapon not as a means of violence, but as an arbitrary, meaningless machine to be analyzed with a technical—not emotional—perspective.