The short answer: because the earliest proof of the theorem based on axioms, which appears in Euclid Elements book 1 proposition 47, has an ancient commentary that attributes the proof to Pythagoras. A biographical tradition represented in Diogenes Laertios also attributes knowledge of the theorem to Pythagoras, though that's much shorter on details.
The longer answer: evidently you're well aware that there's evidence of earlier knowledge of the theorem from ancient Babylonia. A couple of Indic texts may also be earlier (early Indian texts are notoriously hard to date, and routinely get violently up-dated by parties with vested interests), and it shows up in Chinese texts two or three centuries after Euclid.
The trick is that there are several forms of the theorem to think about. You've got special cases of right-angled triangles which satisfy a^(2)+b^(2)=c^(2) for specific cases of integer a, b, and c; and the general case, where it is proved for any right-angled triangle with sides of any (non-integer) length. In addition, we can add reverse proofs, which use geometric techniques to find integer Pythagorean triples.
What people really mean when they say that the Babylonians knew the theorem is that they knew the special cases: the evidence there consists of lists of Pythagorean triples, not of a general proof. The earliest general proof is the one in Euclid, and since that's attributed to Pythagoras in the scholia, that's the reason why the theorem's name has stuck around.
If you go and compare the Indian and Chinese cases you'll see that not only are they not general (they're mostly reverse proofs and collections of triples, though there is mention of a Chinese general proof for isosceles right-angled triangles dating to the Han era), they're totally different from the Euclidean proof. This points to the conclusion that while the truth of the theorem was known throughout early Eurasia for specific integer Pythagorean triples, it took some time for general proofs to come along. And come they did: but that doesn't mean that the general proofs we find in different cultures are dependent on one another. Remember that several hundred separate proofs are known for the theorem today. I find it very easy to believe that proofs were developed independently in Greece, China, and India, centuries after the special cases were disseminated.
OK, that's one side of the question. The other is: why Pythagoras? The proof comes from Euclid, and the evidence connecting it to Pythagoras isn't exactly solid. Ancient sources on Pythagoreanism are very unreliable, and even when they're trustworthy they relate to the post-Pythagorean tradition, often centuries later, not to Pythagoras himself. The word of the Euclid scholia just isn't good enough.
The answer here is that while Pythagoras himself almost certainly didn't know a general proof, his cult was heavily invested in numerology and, by extension, mathematics. It's perfectly possible that the general proof originated with his followers some centuries after the man himself died. Upward attribution would see to it that it got credited to Pythagoras; this would at least explain why the Euclid scholia and Diogenes Laertios associated it with him. If you look at other ancient testimony on Pythagoras and the theorem, you'll see that it only relates to special cases, and in particular the 3-4-5 case: it seems that for Pythagoras, the numbers 3, 4, and 5 took on mystic associations, and he allegorised 3 as representing Osiris (male), 4 as Isis (female), and 5 as Horus (synthesis, marriage). At any rate that's the explanation we find in Plutarch On Isis and Osiris 373f-374a, ch. 56. Actual Pythagoreanism was first and foremost a pretty weird mystic cult. But it seems that a sect that broke off in the 5th century BCE, the mathematikoi or "disciples via learning", devoted themselves a bit more to the numerical research and a bit less to the weird numerological beliefs. If anyone, they're probably the ones responsible for the theorem.