What you could do is reuse the DynamicTypeDescriptor class described in my answer to this question here on SO: PropertyGrid Browsable not found for entity framework created property, how to find it?
like this:
DynamicTypeDescriptor dtp = new DynamicTypeDescriptor(typeObj);
// get current property definition and remove it
var current = dtp.Properties["ThePropertyToChange"];
dtp.RemoveProperty("ThePropertyToChange");
// add a new one, but change its display name
DynamicTypeDescriptor.DynamicProperty prop = new DynamicTypeDescriptor.DynamicProperty(dtp, current, obj);
prop.SetDisplayName("MyNewPropertyName");
dtp.AddProperty(prop);
propertyGrid1.SelectedObject = dtp.FromComponent(obj);