The following are two examples of how what we call 「Greek alphabet」 has been a more complex system of written communication in different parts of the world, for languages which were not Greek, and in societies which were not originally Hellenic. A script is not necessarily connected with only one language and the alphabet was used in the past for a huge variety of languages, ranging from Phrygian to Judaeo-Spanish. Greek script itself is not originally Greek, and the ancient Hellenes suspected that they owed it to the Phoenicians. Herodotus called the letters 「φοινίκεια γράμματα」  and stated that they came to Greece with the people of king Cadmus. Greeks adapted the Phoenician letters especially by shifting some letter values to vowels which were more important to focus on in an Indo-European kind of language. Through different shapes and formats, the alphabet spread to the West, but also to the East. Here are two interesting adaptations from both sides.
The first interesting case is in the West, in my own Southern Gaul country (South of France nowadays) and Eastern coast of Spain. Long before the Roman invasion, the Ionians from Massalia (Marseille), Nikeia (Nice) or Emporion (Empúries) dealt with populations around, among which were Celtic (Gaul) tribes. This is why Celtic languages were spelled in Greek alphabet before the Roman invasion. One of the sounds used in these languages was the affricate sound /t͡s/ that was not existing in Ionian at that time. Instead of combining a tau with a sigma, Gaulish speakers preferred the combination of a double theta : 「ΘΘ」.
Here is the second case. In the Buddhist and ‘Indo-Greek’ kingdom of Bactria in Central Asia, Bactrian language speakers added the letter ϸ (‘sho’, modern editing capital: Ϸ small: ϸ) to the 24 classical letters of the Greek alphabet that they started to use after Macedonian conquests and Hellenisation of the region. Since Greek didn’t have any letter to represent the sound /ʃ/  which actually existed in Bactrian language , 「ϸ」 has been created for this purpose.
In Sanskrit, the expression 「यवन लिपि」 /jˈəwənəˈlipi/ (or ‘Yavana Lipi’) has been used to refer to Greek script, sometimes applied to local languages in Indo-Greek kingdoms. Such might have been the case for the Greco-Bactrian alphabet.
Unfortunately, modern uses of Greek alphabet didn’t follow this 「ϸ」 inspiration. I always wondered how modern spelling would look like today. We might have modern words like 「(τ)ϸοκολάτα」 instead of 「σοκολάτα」 in Dimotiki, Pontic or Griko, which is not the current case – assuming that foreign introduction of the phoneme would have existed too. But in ‘Yavana Lipi’ such as for Bactrian names, you could read a king’s name like Kanishka spelled 「ΚΑΝΗϷΚΕ」. 「Ϸ」 is now part of Greek block in Unicode  and is clearly discriminated from Icelandic thorn.
 /pʰojˈnikejaˈgrammata/ ‘Phoenician letters’
 English spelling equivalent is ‘sh’.
 Indo-Iranian branch of IE family.
 Here’s a previous project for adding the letter 「ϸ」 to Unicode ⇒ http://www.unicode.org/L2/L2002/02056-n2411.pdf
Ill. Credit: N. Sims-Williams ‘A Bactrian deed of manumission’, Silk Road Art and Archaeology