The content of the month of Adar is expressed in its name, just as the essence of each thing is expressed in its corresponding Hebrew name.
Although the Talmud says that the names of the months "came up with them (i.e., with Ezra and those who returned from exile from) Babylon," which seems to indicate that they are not Hebrew names, however, since there are several explanations from our sages linked to the names of the months, we must say that what "came up from Babylon" was not the name itself, but the connection between the names and the months themselves (as periods of time in the year).
Furthermore, it is not appropriate to say that this connection arose in Babylon, but rather that the Jewish people remembered and revealed during their exile in Babylon the connection that already existed between the names of the months and their respective times.
The name Adar is connected with the word Adir (as in Psalm 93, "Adir - Mighty in the heights, God")
This indicates that the theme of the month of Adar is power and strength. Applied to the service of God, this teaches us that everything we do in terms of Torah study and the observance of mitzvot should be done with strength and determination.