Because they weren't religions in the modern or Abrahamic sense. They were essentially a collection of traditions and rituals that were never canonised on a single text, like the Old and New testaments.

In the Greek and Roman worlds priests and state officials weren't interested in what you believed, what was important to them was that all citizens upheld the rituals which essentially symbolised and embodied the values and culture of the state and the dominant people. Your personal worldview and the way you chose to live your life was the domain of the philosophers.

But i'm not a historian, so maybe you should wait for a more qualified answer.

Edit: typos

The Greco-Roman religion(s)

There's your clue: you yourself recognise that "religions" is perhaps a more accurate term than "religion" in this case. There was no "Greco-Roman religion" in the sense of a monolithic entity with a unified set of doctrines and beliefs. Quite the opposite: the stories and beliefs about a particular god in one city might be completely different from the stories and beliefs about the same god in a different place.

Take your example of Buddhism: there are several different schools of Buddhism, but they all hold certain specific beliefs in common, such as the Fourth Noble Truths. What did the followers of this "Greco-Roman religion" have in common? Polytheism? Animal sacrifice? These could just as easily apply to the Aztecs. Religion in the Greek and Roman worlds was highly localised, with each city having its own traditional ways of venerating their gods. There were also mystery religions, cults whose followers had to be specially inducted, unlike most religious practises, which were seen as civic or private duties to be performed by all. As you can see from the terminology, these cults were essentially religions in their own right, although unlike in the modern world, religions were not seen as mutually exclusive.

So, there is no name for "the Greco-Roman religion" because it was not a single unified religion. Rather, there was a hugely diverse array of beliefs and practises across the classical Mediterranean, many of which were indeed similar, but far from homogeneous, and this diversity did not challenge the validity of any individual local custom.

In Rome one night refer to the customs rather than to religion as such. Consider the Mos Maiorum (customs of the majority) which was a Roman name for their civic religion. To a Republican Roman like Cato the Elder there would not have been a distinction between civic and religious festivals. I'm on vacation now or I would respond further, but looking into the Mos Maiorum would be a good place to start.

It's worth noting that "Hinduism" in the religious sense is a term originating in the 19th century; before that India's main religion(s) didn't really have a name either.

Moreover, the Greeks and Romans themselves wouldn't have seen the distinction between their own beliefs and those of other polytheistic cultures as starkly as one might think. Under the Interpretatio Graeca and Interpretatio Romana, the gods of other cultures tended to be understood as different names for their own gods, sometimes even when the similarities were fairly superficial. Even the supposed equivalence between the Greek gods and the Roman ones is the result of this sort of searching for correspondences rather that the Romans simply copying the Greek gods wholesale; the Romans understood Mars, for example, in a different (more positive) way than the Greeks viewed Ares.

"Religion" is a modern concept. It's not mentioned in any ancient literature. The word doesn't appear in the Bible, Iliad, Ramayana, or the Upinshads.

The Latin word "religio" includes non-religious activities such as voting and paying taxes. Invoking the word "religion" implies a religious/secular divide that didn't exist in the thought of pre-modern people.

Pre-modern people would talk about the worship of various deities, but nobody thought this worship took place in a clearly defined part of civic life. There was no way to say "John belongs to religion x, but Jane belongs to religion y." The category "religion," as distinct from politics, law, economics, or family tradition didn't exist.

The concept of religion was introduced during the Enlightenment. By that point, ancient Paganism had expired. Because it wasn't an active religion, the traditions were conveniently clumped together. The same thing happened, and continues to happen, to non western religions. Hinduism is an example of this.

This review of "The Invention of Religion in Japan" by Jason Ānanda Josephson discusses how awkward it is to impose the modern, Western concept of religion on to non-Western societies. More reviews [here] (http://muse.jhu.edu/login?auth=0&type=summary&url=/journals/monumenta_nipponica/v068/68.2.reader.html ), here, and here.

Here is a book review of "Before Religion: A History of a Modern Concept?" by Brent Nongbri. It discusses how the concept of religion evolved from modern imperialism, and how it effects modern public discourse.