Why were the Ionian Greeks called the Ionians Greeks when the Sea of Ionia is on the other side of Greece?

To elaborate on Niko Vasileas’ answer and Michael Anderson’s answer:

Nominative Iōn, Genitive Iōn-os, Adjective Iōn-ikos or Iōn-ios refers to the tribe of Ionians.

Adjective Iŏn-ios refers to the sea, and is traditionally derived from the lover of Zeus, Io (mythology): Nominative Iō, Genitive Ious < *Iŏ-os. Io, transformed into a cow, is supposed to have crossed both the Bosphorus (“ox passage”) and the Ionian Sea, before being restored to human form.

Io (mythology) – Wikipedia: Juno, Jupiter and Io by Gerbrand van den Eeckhout.

Grammatically, I’m not convinced by Io; Sardŏnios ‘Sardonic, Sardinian’ is derived from Sard-ō, -ous “Sardinia”, but Sardō did also have a Sard-ŏnos genitive. So as Nikos says, it’s potentially something else. At any rate, it is unlikely to have anything to do with the Ionian tribe.