Were these persons who lived in Indian Territory, or Louisiana? I ask because this is posted as a query about persons from LA. Perhaps I am mistaken. However, note that persons living in Louisiana were not included on the Drennan Roll.

The Roll created in the 1850s were created by Indian agent John Drennan, of NW Arkansas on the border of the Cherokee Nation, who oversaw many affairs pertaining to Indian Territory. The Saline District was part of the Cherokee Nation, located in what is now known as eastern Oklahoma. These persons (including the Wrights listed,)resided in the Saline District if they were on the Drennan Roll. The location of the Saline District is approximately around the vicinity of Rose, Oklahoma.

Regarding their names---they are written as they were called. There was no English version of their names. One whose name was:
A-Kea-yah-a-akee was called by that name. It does not translate into Johnson or an English equivalent. It is possible that subsequent generations from that family line, may have later anglicized their surname, but that is not a guarantee, either. There are still persons who have traditional names, unchanged.

If the Wright family was in the Saline District of the Cherokee Nation in the 1850s, did they remain in the the same district?

The link below speaks a littlbit about some aspects of the Saline District.