The usual interpretation is that it was true after all. The sceptical computer operators never believed in God or that the universe would end when the book was finished, but the stars going out vindicates the monks. The moral of the story could be seen as "don't knock someone else's religion: you never know, it might be real after all".
Another interpretation I found here
is as follows.
These are Tibetan Buddhist monks. Buddhism in general is not concerned with "God." Enlightenment is their goal and compassion (understanding the suffering of other beings) is a major way of achieving enlightenment. Since these monks are not concerned about "God," their work of trying to discover the name of "God" through the iteration of all the names is not for their benefit at all. Either “God” is confused about what its real name is, or this is a typically cruel trick of some authoritarian patriarchical deity. But for the monks, it’s a moot point.
When the atheist monks finished the book of names, they had achieved the goal, not actually of naming some deity which they do not even believe in, but of realizing that "God" is unnameable because, in fact, there is no "God."
When the stars "go out" at the end, it us not really the end of the universe (which would have really been overkill by a wrathful deity in wiping out the entire universe, instead of just Earth). Also it would have been difficult for this deity to coordinate the timing of the extinguishing of the stars since the ancient light streaming in is millions of light-years old and each star is more or less different in distance from Earth, and the exact time that the monks’ woulf finish was indeterminate.
I think this is the atheist Clarke using technology to debunk the notion of “God.” The light of the stars going out is a poetic, allegorical kind of extinguishing. What is going out is the necessity for imagining that God is necessary at all.
Basically, it's one of those thought-provoking stories whose point is not entirely clear and may be left, at least to some extent, up to the interpretation of the individual reader. I don't know if Clarke himself ever said anything as to how he expected this story to be interpreted.