The range you are using is Greek extended. You want the range from 0370 to 03ff. From the page you quoted:
0370..03FF; Greek and Coptic
1F00..1FFF; Greek Extended
function is_greek(name){
var greek = /[\u0370-\u03ff]/;
return greek.test(name);
}
> is_greek("α")
< true
1
solved RegExp name validation using hexadecimal metacharacters