Searle writes this assuming he can rely upon his theory of Intentionality, which is a theory of how some kind of mental state can refer to or otherwise "be about" something else, even something that does not exist. For our purposes, we can ignore this issue. However, one should note that Searle has a theory which drives him to be a description theorist about names: he says intentional states, which must include thinking about proper names, are always states with meaning and part of a network of meanings. So, he concludes, they must be explained in terms of meaning.
Analysis
For Searle, the real issue between descriptivism and the causal theory is that the description theory claims proper names refer by meeting certain internal standards (that is, meaning is in the head!). The causal theory, he claims, makes reference something external it is not a matter of satisfying internal mental conditions. (Martinich 2006)
Searle claims the Kripkean baptism depends upon descriptions in a way, since it is the social convention and the ability of the person to recognize the thing being baptized, and not any purely physical causal account, that is required for the naming.
There is also, Searle claims, the sneaking in of the intention (goal) of the speakers involved. One must have the goal of referring to this thing and not that (there will be many things in the room, all with causal relations to the speaker), the hearer must have the same goal, and so on.
Searle points to Gareth Evans' problem as a good example of a problem for the causal theory. Evans pointed out that "Madagascar" originally referred to part of Africa. It came to be used to refer to the island we now call "Madagascar." How does such a switch work on the causal theory? There was no new baptism, Evans claims.
Searle also offers a clever response to Kaplan regardings Ramses VIII. This illustrates Searle's notion that reference requires a network of meanings. Searle also imagines a tribe where the members do not speak of the dead, and all teaching is done by ostentation (pointing) at the thing named. He claims the causal theory never applies! This is because there is never a chain that doesn't include the person perceiving the thing being named (no "hand me down" references). And so, the description theory works for everything here. Note he's imagining ...