The phrase כי שמי בקרבו is drawn from the pasuk warning Israel to heed the angel sent before them because God's name is within him (the Ramban (Shemot 23:20-21), the Sforno (Shemot 23:20-21)), and the Ibn Ezra (Shemot 23:20-21) explains that every angel executes God's command without deviation, so that heeding the angel's voice is tantamount to heeding the voice of God Himself, since God's glorious name rests within him as a point of closeness even while traveling in the midst of the camp.
The Ramban explains that this angel will not pardon transgression against him because rebelling against his word is rebellion against the great Name dwelling within him (the Ramban (Shemot 23:20-21)), while the Sforno likewise states that the angel lacks the capacity to forgive offenses against God's honor (the Sforno (Shemot 23:20-21)); Rabbeinu Bahya identifies this angel as Michael and explains that being called by this Name means being called 'the captain of the host of the Lord,' parallel to a house being called by God's name, while still cautioning Israel to guard against sin since forgiveness itself remains in God's own hand (Rabbeinu Bahya (Shemot 23:20)).
Rashi connects this warning to the sin of the golden calf, teaching that here Israel was informed in advance that they would eventually sin and that the Shechinah itself would declare, 'for I will not go up among you' (Rashi (Shemot 23:20)), a reading echoed in the Midrash explaining that an angel was sent only after Israel served idols, when Moshe protested that God's own Presence must go with them rather than a mere angel (Shemot Rabbah 32:3, Midrash Tanchuma Buber, Mishpatim 12:1).
Chazal elsewhere extend the principle that an angel bearing God's name shares in Israel's suffering, as the Mekhilta teaches that whenever Israel is enslaved the Shechinah is, as it were, enslaved with them, deriving from 'in all their trouble He was troubled' that this applies to individual as well as communal distress (Mekhilta DeRabbi Yishmael, Pischa 14:19), a pasuk also read in Yeshayahu itself describing the angel of His Presence delivering them out of love and compassion (Yeshayahu 63:9).
The Gemara in Sanhedrin records that Rav Idit answered a heretic's challenge on the verse 'come up to the Lord' by identifying this figure as the angel Metatron, whose name is like that of his Master precisely because 'My Name is in him,' yet insists that Israel never substituted worship of this angel for worship of God, relying on the assurance that God's own Presence must go with them (Sanhedrin 38b:19-20); this same angel of God is described protecting those who fear Him in Tehillim (Tehillim 34:8).
The Zohar extends the identification of 'the angel of God' to the Shechinah itself, noting that when the Matrona (Shechinah) travels all travel with her, and that every message of the King passes through this supernal gate (Zohar, Beshalach 12:149-150).
Later commentators carry the theme further: the Rashbam notes that Scripture repeatedly calls an angel by the divine name because an agent is like the one who sends him, citing 'for My Name is in him' alongside the angel who appeared to Moshe in the burning bush (Rashbam on Bereishit 18:1); the Sefat Emet reads the verse as teaching that holiness is hidden even in mundane action, since every deed contains God's vitality and is itself a kind of angel or agent sent to fulfill His will, requiring heightened guardedness (Sefat Emet, Shemot, Mishpatim 1:3, Sefat Emet, Vayikra, Vayikra 1:2).
Mishneh Halachos (12:481) holds that one who studies Torah lishmah and engages in halachah becomes, in a sense, a chariot for the Holy One, and may be called 'an angel of the Lord of Hosts,' because such a person embodies Torah and the Shechinah speaks through him — extending the theme of God's name dwelling within an agent to the Torah scholar himself.