At first glance, the title of this one functions on a pretty basic level: it tells us what kind of poem it is—kind of like titling a sonnet… "Sonnet." However, upon closer inspection (time to get out those magnifying glasses, Shmoopers), this title functions on another level as well.
Traditionally, an aubade celebrates the arrival of dawn—the light of day pushing away the darkness of night. It can also be a kind of morning love poem. The typical situation has something to do with lovers parting (sometimes out of necessity) at sunrise. There might be a little sadness in the departure, but at least their love endures. Now, let's assume you already knew what an aubade was. When you read Larkin's "Aubade," did he give you what the title set you up to expect? Nope. There are some pretty major aubade-components missing.
First of all, Larkin's speaker is alone and we don't get the sense that there was any lover in the picture. He worked, drank, slept a bit, and woke up depressed in the wee hours of the morning. If we stretch it, we could say that he's not alone; death is with him in the room (and everywhere else, really). When morning does arrive, our speaker tells us that, "One side will have to go," but it doesn't seem like death gets the message because it feels like he's still hanging around. Worst sleepover ever.
So, what does this title do? It sets up an expectation, and then doesn't deliver. This creates a sense of disappointment and that disappointment hangs over the poem like a dark cloud. It's as if Larkin, with this title, is trying to let us know that we aren't going to get what we expect. There is no great payoff in life (or after it); there is no lover; there's only death. There is no celebration of dawn's arrival. In fact, the sun doesn't even show up ("The sky is white as clay, with no sun")! The arrival of day doesn't signify the conquest of life's light over the death's darkness. It just announces another day going through the mundane motions of daily life until death—permanent night—finally arrives. Now, all aboard the good times train.