DON DeLILLO is a formidable prose stylist; as Fred Allen once said of another literary craftsman, "He writes so well he makes me feel like putting my quill back in my goose." From time to time DeLillo thinks as keenly as he writes, and it is in these moments that The Names, his seventh novel, achieves its greatest power and interest. Unfortunately, though, these moments are concentrated in the first of the book's three principal sections, leaving the reader to plow through the remaining two- thirds with comparatively slight reward. The Names is an accomplished and intelligent novel, the work of a writer of clear if chilly brilliance, but it takes on too many themes and wanders in too many directions to find a coherent shape.

It is for his second novel, End Zone, that DeLillo is perhaps still best known. There his subject was the American propensity for institutionalized, ritualistic violence, and his metaphor for it was intercollegiate football. In The Names he is once again concerned with violence, but this time on an international scale. The narrator, James Axton, is a 38-year-old former free-lance writer who now works out of Athens as "associate director of risk analysis, Middle East," for a group "writing political risk insurance in impressive amounts." His clients are large corporations who want to insure their investments against worldwide political turmoil, and his job is to evaluate the risks involved: "I like the job, even the travel. . . . This is where I want to be. History. It's in the air. Events are linking all these countries. What do we talk about over dinner, all of us? Politics basically. That's what it comes down to. Money and politics. And that's my job. . . ."

In Athens, Axton is a member of a small community of Americans in similar lines of work, "the living to be made in terror." They are on the front lines, witnesses to and occasional victims of the seemingly endless process of disintegration and chaos. DeLillo describes their situation pungently:

"There was a protocol of coping, of making do. . . . I was learning that reticence was fairly common in such matters. There was a sense in which people felt it was self-incriminating to speak out against these violations. I thought I sometimes detected in people who had lost property or fled, most frequently in Americans, some mild surprise that it hadn't happened sooner, that the men with the six-day beards hadn't come much earlier to burn them out, or uproot the plumbing, or walk off with the prayer rugs they'd bargained for in the souk and bought as investments--for the crimes of drinking whiskey, making money, jogging in shiny suits along the boulevards at dusk. Wasn't there a sense, we Americans felt, in which we had it coming?"

So long as DeLillo is describing this community and its perilous, morally equivocal position, The Names is entirely successful; his portraits of individual members of the community are sharp and true, his depiction of a world on the brink is wittily clinical, his dialogue is crisp and interesting. But he insists on going deeper than that, and when he does the novel drifts in various uncertain and not especially rewarding directions.

Axton is separated from his wife, who lives on "Kouros, an obscure island in the Cyladic group," with their 9-year-old son. There she works at an archaeological dig, and there Axton discovers evidence of cult murders. The murders come to obsess him. He believes that the cult, which seems to call itself "The Names," is "the only thing I seem to connect with." When at last he tracks down a member of the cult and asks if he can disclose its name, he receives this reply: "No, impossible. Nameforms are an important element in our program, as you know. What do we have? Names, letters, sounds, derivations, transliterations. We approach nameforms warily. Such secret power. When the name is itself secret, the power and influence are magnified. A secret name is a way of escaping the world. It is an opening into the self."

This -- the mystery of naming, the mystery of language and words -- is the theme to which DeLillo returns over and again. His Americans are people who are in the world yet unconnected with it because they have not bothered to learn any languages--which is to say any cultures, any realities--save their own. DeLillo asks the question, "How do you connect things?" and supplies the answer: "Learn their names." At the end Axton stands at the Parthenon: "People come through the gateway, people in streams and clusters, in mass assemblies. No one seems to be alone. This is a place to enter in crowds, seek company and talk. Everyone is talking. I move past the scaffolding and walk down the steps, hearing one language after another, rich, harsh, mysterious, strong. This is what we bring to the temple, not prayer or chant or slaughtered rams. Our offering is language."

That is an appealing observation and an elegant piece of prose, but DeLillo comes to it by so circuitous a route that many readers probably will lose patience along the way. To describe The Names as self-indulgent is perhaps unfair, but DeLillo allows Axton's quest to follow too many dead-end lanes and to wander too far from the subject about which he is most provocative, that of the rootless and cynical American internationalists. Of Greece he writes: "The deep terraces spill over with lantana and jasmine, the views are panoramic, the caf,es full of talk and smoke into the early hours. Americans used to come to places like this to write and paint and study, to find deeper textures. Now we do business." This is the core of The Names, and when the novel is clearly focused thereon it is splendid work; but DeLillo goes on too long, and too far afield, so that in the end The Names is impressive but shapeless.