how to use a variable name in checkpoint?

A neat trick that HKosova showed me recently is that, if you're using JScript/JavaScript, you can change dot syntax to bracket syntax.  So, try the following:

function CheckFeatures()
{
var i,featureItem,featureName;
SelectFeatureTree()
for(i=0;i<12;i++)
{
featureItem = FeatureTree.wItems.Item(0).Items.Item(3).Items.Item(i);
featureName = featureItem.Text;

featureName = name(featureName)

Regions[featureName].Check(Aliases.SLDWORKS.dlgFeatureParameters.Window("SysListView32", "", 1));

}

Now, this assumes that you actually have regions stored in Stores.Regions named for each of your feature names.  However, this SHOULD work.  Give it a go.

If that doesn't work, you might have to resort to eval

function CheckFeatures()
{
var i,featureItem,featureName, featureRegion;
SelectFeatureTree()
for(i=0;i<12;i++)
{
featureItem = FeatureTree.wItems.Item(0).Items.Item(3).Items.Item(i);
featureName = featureItem.Text;

featureName = name(featureName)

featureRegion = eval('Regions.' + featureName);

featureRegion.Check(Aliases.SLDWORKS.dlgFeatureParameters.Window("SysListView32", "", 1));

}

I think you can try

Regions.Items(featureName).Check(Aliases.SLDWORKS.dlgFeatureParameters.Window("SysListView32", "", 1))

instead of  eval.