You heard correctly and I am happy to share some points about this special month that we are now beginning, the month that leads up to Rosh Hashanah.
The name of the month is “Elul” and it is the sixth month of the Jewish year (we count the months of the year starting with Nissan, the month of Passover, since that is when we became a “nation” through the Exodus from Egypt followed by our receiving the Torah at Mount Sinai).
We find that several acronyms are quoted from verses in reference to the month of Elul. For example, the first letters of the Hebrew words "Ani L'dodi V'dodi Li — I am my Beloved's and my Beloved is mine" (Song of Songs 6:3) — spell "Elul", and are seen as a reference to God's “closeness” to us during the month of Elul.
Despite the word "Elul" — and the names of all of the Jewish months that we use nowadays — being of Babylonian origin, it is kosher and correct to refer to the months by these names, and even to learn the essence of the months from these names.
The names of the Jewish months came into use when the exiled Jews of Babylon, who spoke Aramaic, returned to the Land of Israel in the time of Ezra. Previously the months had no names, but were referred to by number.
Nachmanides says these names are of Persian origin, but that doesn't preclude their also having Aramaic roots, as the Persian Empire succeeded the Babylonian Empire, and the language of Babylon was Aramaic.
So, how can the verses in the Hebrew Torah hint to Aramaic words? Actually, Aramaic is a sister language of Hebrew. According to the Kabbala it is actually a dialect of Hebrew. That is why most of the Oral Law is written in Aramaic, or in Mishnaic Hebrew which is a mixture of Aramaic and Biblical Hebrew.
In addition, the word Elul means "search," because during the month of Elul we search our hearts for evil and repent in preparation for Rosh Hashanah.
