curl --request PUT \
  --url https://{db}.{region}.api.lancedb.com/v1/tables/{name}/schema/columns \
  --header 'Content-Type: application/json' \
  --header 'x-api-key: <api-key>' \
  --data '{
  "alterations": [
    {
      "path": "outer.inner",
      "rename": "new_name",
      "data_type": {
        "type": "int64",
        "fields": [
          {
            "name": "<string>",
            "type": {},
            "nullable": true
          }
        ],
        "length": 123
      },
      "nullable": true
    }
  ]
}'

This response does not have an example.