Edda means sage
Both the name of the elder womman Edda and the name of the Edda book match the Sanskrit’s addha (clearly) and addhAti (sage)
अद्धाति m. addhAti sage
Sanskrit dictionary
[«previous (A) next»] — Addha in Sanskrit glossary
Source: DDSA: The practical Sanskrit-English dictionary
Addhā (अद्धा).—ind. [atyate at taṃ santataṃ gamanaṃ jñānaṃ vā dadhāti kvip Tv.]
۱) Truly, clearly, surely, undoubtedly, in truth, really, certainly, indeed; को अद्धा वेद (ko addhā veda) Ṛgveda 1.129.6. अद्धा श्रियं पालितसङ्गराय प्रत्यर्पयिष्यति (addhā śriyaṃ pālitasaṅgarāya pratyarpayiṣyati) R.13.65.