Who was speaking to Israel in the Old Testament?
Yahweh.
If you divide God into three (or more) persons, which one was speaking?
That depends on the scripture.
Many times Malek Yahweh spoke, face to face, with the prophets, in human form.
I can't recall any one of them where God identifies himself and says "I am the Father" or "I am the Son" or "I am the Holy Spirit" ... that just wasn't the form of address or introduction used. Are you thinking of something I missed?
God was known by different names and titles in the OT.
Here are a few...
God The Father was known as:
• Yahweh
• Elohim ‘God’
• El Elyon ‘God Most High’ (Gen 14.18, 19, 20, 22)
• El Olam ‘God Eternal’ (Gen 21.33
• Adonai Yahweh ‘Lord Yahweh’ (Gen 15.2, 8)
God The Son was known as:
• El Shaddai ‘God of Mighty Ones’ (Gen 17.1, 28.3, 35.11, 43.14, 48.3, 49.25; Exo 6.3)
• Elohim ‘God’ (Gen 16.13, 22.12, 31.13; Exo 3.6)
• The Malek Elohim ‘The Messenger of God’ (Gen 21.17; 31.11)
• The Malek Yahweh ‘ The Messenger of Yahweh’ (Gen 16.7, 9 - 11; 22.11, 15)
• Debar Yahweh ‘The Word of Yahweh’ (Gen 15.1, 4; Exo 9.20, 21)
God The Spirit was known as:
• The Ruach of Elohim ‘Spirit of God’ (Gen 1.2)
• The Ruach of Yahweh ‘Spirit of Yahweh’ (Gen 6.3)