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);