One very simple method, if you don not fear the command line, is to use ogrinfo http://www.gdal.org/ogrinfo.html with OGR SQL dialect http://www.gdal.org/ogr_sql.html.
Take a shapefile with columnn named "foo"
ogrinfo -al -so test.shp
INFO: Open of `test.shp'
using driver `ESRI Shapefile' successful.
Layer name: test
Metadata:
DBF_DATE_LAST_UPDATE=2017-06-13
Geometry: Point
Feature Count: 1
Extent: (350.000000, 372.000000) - (350.000000, 372.000000)
Layer SRS WKT:
(unknown)
foo: String (5.0)
Rename column with ogrinfo
ogrinfo -sql "ALTER TABLE test RENAME COLUMN foo TO bar" test.shp
Check the result
ogrinfo -al -so test.shp
INFO: Open of `test.shp'
using driver `ESRI Shapefile' successful.
Layer name: test
Metadata:
DBF_DATE_LAST_UPDATE=2017-06-13
Geometry: Point
Feature Count: 1
Extent: (350.000000, 372.000000) - (350.000000, 372.000000)
Layer SRS WKT:
(unknown)
bar: String (5.0)