There was just as much analysis of Joseph Ratzinger's choice on Benedict as there was about Jorge Mario Bergoglio's choice of Francis. The popular press, however, took little notice of the possible reasons for "Benedict" as it was too busy vilifying Ratzinger. (As always, the most serious press bias is not in reporting incorrectly but in what they choose to ignore.)
There is an interesting tension in the choice of the name.
The most obvious possibility for the inspiration of the name is Saint Benedict whose Benedictine rule is believed by many, including me, to have played a major role in the creation of the new European civilization out of the remnants of late antiquity. Pope Benedict XVI's speculation that God was perhaps going to prune the church so that it could grow aligns with this. He drew on a motto found at the frequently destroyed Benedictine Abbey at Monte Cassino, "Succisa Virescit", which means, roughly, "cut down, she grows back".
Politically, we could interpret that as advice for how those in the church should respond to a larger culture that attacks them. We might, as the Benedict option popularized by Rod Dreher would have us do, form separate communities within the greater civilization. These wouldn't be completely cut off, indeed it would be impossible that they could be. Rather, the point would be that they would be little communities where certain core values were embodied such that they could sprout forth and grow when the larger civilization around them calms down.
A less obvious connection to make with the name Benedict is with Pope Benedict XV. At first glance, we might be tempted to think this comparison would only reinforce the first. Benedict XVI's papacy coincided with the First World War and we might think this just another instance of church institutions preserving culture while the culture outside committed suicide. But Benedict XVI did not recommend any withdrawal from the larger culture. Instead he emphasized the need to focus on basics by remaining neutral in political struggles, promoting peace and, when war breaks out as it inevitably must, the ease of suffering.
I wonder if there isn't, behind Benedict XV and Benedict XVI, a subtle shift in attitudes towards Thomism. Beginning with Pope Leo XIII, there was a tendency to emphasize the second part of the second part of the Summa Theologiae. That section of the text focuses on the virtue of justice and is the source of the Church's social teaching. Leo XIII did much to promote the revival of Thomism for this purpose. However, Thomism was redirected towards epistemology so as to provide a counterfoil to modernism under the Papacy of Pius X. Benedict XVI, without directly opposing his predecessor Pius X, emphasized the concern for justice that had inspired Leo XIII.
And Benedict XVI? I think he may have intended to de-emphasize some of the work of his predecessor John Paul II, now Saint John Paul II, without directly contradicting him. He was very close to John Paul and loved him dearly but, I suspect, was also aware of certain shortcomings. He sought to de-emphasize certain aspects of John Paul's legacy without directly contradicting the man he revered.
If I am right, we can see subtle corrections of John Paul II is some of Benedict XVI's acts. Deus caritas est, then is a redirection away from the theology of the body. I think that, like John Paul II, Benedict saw Humanae Vitae as a "catechetical disaster" but also recognized that it would be a pastoral disaster to rescind it. The theology of the body was John Paul's attempt to salvage what could be salvaged and then refocus attention in a more useful direction. If I am right, and base my arguments only on intuition at this point, Benedict XVI revisits the issue in Deus caritas est. The redirection here is not in what is said but in what isn't said. Benedict makes his arguments about eros without talking of any theology of the body as a subtle way of letting us know that he doesn't think such a move is necessary or helpful.
I also think that something similar happens with Caritas in Veritate. Again, John Paul II and Benedict were left cleaning up the missteps of Paul VI. This time the offending encyclical is Populorum progressio. It also is a catechetical failure. John Paul II sought to redirect matters by rethinking and attempting to improve our understanding of development in his encyclical Solicitudo rei socialis. Benedict XVI, while sympathetic, believed that any discussion of development or progress will necessarily force to the Church support specific political initiatives to her possible detriment. Again, the correction of his predecessor is not in what he chooses to say in Caritas in Veritate but in what he chooses not to say. The more abstract arguments we see in Benedict's encyclical are a deliberate drawing back from what he does not wish us to conclude.
Underneath all this may be a claim about what Thomism should and should not be. John Paul II emphasized the philosophy of Thomas as a philosophy of being, "whose transcendental value paves the most direct way to rise to the knowledge of subsisting Being and Pure Act, namely to God". The heading for this post is the Italian of what he goes on to say, "we can even call this philosophy the philosophy of the proclamation of being, a chant in praise of what exists". Fergus Kerr, whom I draw heavily on here, notes that the phrase is even more beautiful in Italian.
Beautiful it is but I think Benedict XVI thought it was just wrong to think that Thomas's philosophy of being was sustainable. To emphasize being, which is to say the ontology of Thomas, was to make a mistake parallel to that Pius X made in emphasizing his epistemology. Benedict XVI thought that 20th century philosophers, principally Heidegger, had issued a challenge that the ahistorical notions of being that we find in Thomas simply could not answer. He thought that focusing on Thomas as a philosopher of being was a foolish and naive project pursued by an otherwise brilliant pope. I think that is right.