The correct option is 2 only.
Explanation
Ashokan inscriptions serve as the most authentic source of Mauryan history. The identification of the king within these texts relies heavily on royal epithets rather than his personal name.
Statement 1 is Incorrect: The personal name "Asoka" does not appear in every inscription. In fact, it is absent from the Major Rock Edicts and Pillar Edicts. The name "Asoka" is explicitly mentioned only in a few Minor Rock Edicts, specifically those found at Maski, Gujjara, Nittur, and Udegolam.
Statement 2 is Correct: In the majority of the inscriptions, the emperor refers to himself using the titles Devanampiya (Beloved of the Gods) and Piyadassi (One who looks with kindness/affection). It was the discovery of the Maski inscription in 1915 that definitively confirmed that the title Devanampiya Piyadassi referred to the Mauryan Emperor Ashoka.
Key Takeaway: The personal name "Asoka" is rare in epigraphic records, appearing only in the Minor Rock Edicts of Maski, Gujjara, Nittur, and Udegolam; elsewhere, the titles Devanampiya and Piyadassi are used.