How did the Sages know the names of particular angels?

The Book of Genesis relates events in which angels visited Gentiles. For example, the angels Gabriel and Rafael came to the family of Lot in Sodom. (See Rashi on Genesis 18:2.) Gabriel was the angel that came to destroy the metropolis. Rafael was the angel that came to save Lot and his daughters from the destruction. Likewise, we see in Genesis that when Hagar ran away, several angels came to give her messages and instructions from G-d. (See Rashi on Gen. 16:7-13.) Why was she not afraid? Because she saw angels in the home of Abraham and Sarah on a regular basis.

We see from the Hebrew Bible and Midrash that many of the Biblical prophets personally encountered or interacted with angels. These include Abraham, Sarah, Jacob, Moses, Aaron, Joshua, Isaiah, Ezekiel, Zechariah, Daniel, etc.

The angelology taught by the Sages was based on prophetic experiences and Divinely-inspired insights of special individuals among them. There have been special individuals in history who reached very high levels of righteousness and perfection. Rambam explained in Mishneh Torah that some people can reach a high level of spiritual perfection. When this happens, G-d rewards them with a spirit of prophecy. In that state of awareness, the person’s consciousness expands beyond the physical world. [1] The heavenly realms and/or heavenly beings and their names are also revealed to the person. This may be with open sight, prophetic vision or Divinely-inspired intellectual insight.

There are numerous examples in the Torah and the Books of the Prophets, and from select Torah Sages over the course of history. Their teachings have been passed down as part of the Oral Torah.

Footnotes:

[1] See Seven Gates of Righteous Knowledge, the Second Gate: “The Gate of Prophecy from G-d,” by Rabbi Moshe Weiner.