3 Semitic men named Aram were listed in the Old Testament of the Bible. The region called Aram was more than likely named after Noah's grandson (Shem's son) or Terah's great-grandson.
Noah > Shem > Aram > Uz, Hul, Gether and Meshech - Genesis 10:22-23:
1 Chronicles 1:17:
17. The sons of Shem: Elam, Asshur, Arphaxad, Lud and Aram. The sons of Aram : Uz, Hul, Gether and Meshech.
Genesis 22:19-24: Terah > Nahor > Kemuel > Aram
19. Then Abraham returned to his servants, and they set off together for Beersheba. And Abraham stayed in Beersheba.
20. Some time later Abraham was told, "Milcah is also a mother; she has borne sons to your brother Nahor:
21. Uz the firstborn, Buz his brother, Kemuel (the father of Aram),
22. Kesed, Hazo, Pildash, Jidlaph and Bethuel."
23. Bethuel became the father of Rebekah. Milcah bore these eight sons to Abraham's brother Nahor.
24. His concubine, whose name was Reumah, also had sons: Tebah, Gaham, Tahash and Maacah.
A third person named Aram showed in 1 Chronicles 7:34 from the tribe of Asher. In contrast, his family lived in modern-day Israel after Joshua
led the Israelites into Canaan (the area within the yellow ellipse on the image).
Jacob (Israel) > Joseph > Asher > Beriah > Heber > Shomer > Aram