Well, particularly for something in ancient Greek, the purpose was to write it in Latin. First, let's start with Ikaros vs Icarus. Both Greek and Latin are inflected languages. The -os and -us endings just indicate that the word is a sedond declension nominative (ie [usually] masculine, subject of the sentence) singular. If you wanted to make Ikaros possessive (the genitive case) that would become Ikarou in Greek and Icari in Latin. So when switching between inflected languages, it's not uncommon to see the ending switch to make it gramatically correct. It also avoids confusion if simialr endings fill different roles in the new language. For instance, Ikaros in Latin would indicate an accusative plural, rather than nominative singular. So it's a bit like the Greek word is actually "Ikar-" and the "os" represents grammar.

So why switch "Ikar-" to "Icar-"? Well, because Ikaros is actually  "Ἴκαρος." Don't forget that Greek uses its own alphabet. To write a Greek word in Latin, they also had to transliterate it into their own language. Latin didn't develop the letter "k" until fairly late, and even then it's just people writing a Greek kappa in Greek words. For most of Roman history, the hard "k" sound was produced by the letter "C." C only ever made that hard sound in classical Latin, the soft "s" sound like "race" only came much later. So to write "Ἴκαρος" in his own language and convey both pronunciation and meaning, a Roman scribe would have to say Icarus.

The trick is, that different languages developed differently over time and their pronunciations drifted further and further apart. Once a foreign word entered the language and a spelling became common, nobody was going back to Greece to make sure they were saying everything correctly.

The problem is further exacerbated if you're writing a word you only ever hear spoken, like an early Roman trying to write down something Celtic, or if you only receive the word after it's transliterated into another script. In case of the former, your stuck with a phonetic guess that might not reflect a later local writing system. In the latter you get issues like the Persian name Cyrus. Cyrus is pronounced like "sigh-ruhs" in English, because we've developed a soft C next to e, i, or y. In Latin it was probably something like "keer-uhs." In ancient Greek that was "Kuros" (because the Greeks and Romans pronounced their u-shaped letters differently) and pronounced "koo-ros" (because upsilon changed in pronunciation over time). They probably got that from either verbal declarations or from Lydian script because the Persians didn't have their own alphabet yet, but in Persian, it was more like "koo-rosh." So over many different languages and many centuries we see a little bit of change with every increment, even though between each step nobody really meant to change anything.