在这里,talking 是现在分词作定语来修饰the student,所以不能加be,加了be,就成了这样：
The student is talking with the teacher is Tom.---一个主语同时带两个同样的（系）动词,不符合语法习惯,如果非要用be,可以改成两个句子：The student is talking with the teacher, the student is Tom.