Links open with New International Version (NIV) verses. Unless otherwise stated, links applicable in both King James & NIV.

Terah, a Semitic Chaldean, decided to migrate westward from Chaldea (near the Persian Gulf). Prior to this migration, his son Haran died while they were still in Chaldea as it was stated in Genesis 11:28. Apparently, the town where they ended their journey (Haran) was named in honor of the son who died.

While the Bible doesn't state it, it's quite possible that God moved Terah's family moved out of Mesopotamia to keep them safe after the Akkadians attacked the Sumerians.

Genesis 11:31-32:
31. Terah took his son Abram, his grandson Lot son of Haran, and his daughter-in-law Sarai, the wife of his son Abram, and together they set out from Ur of the Chaldeans to go to Canaan. But when they came to Haran, they settled there.
32. Terah lived 205 years, and he died in Haran.

Terah (town) reference:

It's uncertain if it's related to the patriarch Terah, NIV stated a town named Terah in the Sinai peninsula considering it was mentioned in the Exodus route between Hazeroth and Kadesh-Barnea in Numbers 33:27-28 (King James spells it Tarah).