Classes 1 and 2 are easy and straightforward. It's the 3rd conditional that makes things a bit tricky. I'd approach this with a definition query for simplicity. You could do all three separate, but I'll just suggest two.
Add your polygon layer once and symbolize it on the name field. You'll choose null for one value and leave the other to 'all other values'. This should give you the first two classes you want.
Then copy that layer, or add your data a second time. In the properties dialog for the new layer, go to the Definition Query tab and build the appropriate SQL expression to show only polys where name is null. Then on the symbology tab you can once again do categories but this time on the notes field. You'll set the value "NUME EBRAICA" to be your third symbol, and then change the 'all other values' symbology to be blank (as in no fill, no outline). This should then show only polygons where the name field is null and the note field has that value. With this layer above your other in the table of contents, you should have the three color map you want. You could also do a custom symbol for this layer so it's stripes or something and the same null color from the other layer would show through if you wanted.
This method doesn't require modifying the data if that would be an issue, and it should be a bit simpler than trying to symbolize on multiple fields since with that method you must symbolize all possible combinations (though you can group them to only have to set the symbology once).