I think you should use SetAlternativeName function like this:

Field1.SetAlternativeName("名字");

In your code:

...
OSGeo.OGR.FieldDefn Field1 = new OSGeo.OGR.FieldDefn("EnglishName", OSGeo.OGR.FieldType.OFTString);
Field1.SetAlternativeName("YourChineseName");
Field1.SetWidth(16);
...