What is the correct format in JSON, should I quote names also?

Old question, but the OP's JSON (first construction) may have the proper syntax, but it's going to cause trouble because it repeats the key student.

import simplejson

data = '''{
    "class": {
        "number": 2,
        "student": {
            "name": "Tom",
            "age": 1
        },
        "student": {
            "name": "May",
            "age": 2
        }
    }
}'''

data_in = simplejson.loads(data)
print(data_in)

Yields: {'class': {'number': 2, 'student': {'age': 2, 'name': 'May'}}}

Where unique keys student_1 and student_2:

import simplejson

data = '''{
    "class": {
        "number": 2,
        "student_1": {
            "name": "Tom",
            "age": 1
        },
        "student_2": {
            "name": "May",
            "age": 2
        }
    }
}'''

data_in = simplejson.loads(data)
print(data_in)

Yields: {'class': {'student_1': {'age': 1, 'name': 'Tom'}, 'number': 2, 'student_2': {'age': 2, 'name': 'May'}}}

UPDATE:
Agree with @Tomas Hesse that an array is better form. It would look like this:

import simplejson

data = '''{
    "class": {
        "number": 2,
        "students" : [
            { "name" : "Tom", "age" : 1 }, 
            { "name" : "May", "age" : 2 }
        ]
    }
}'''

data_in = simplejson.loads(data)
print(data_in)

JSON requires the quotes. See http://json.org for the specifications.

In particular, the string production is:

string
    '"' characters '"'

The first is valid, if you're unaware you can validate your JSON output online pretty easily here: http://www.jsonlint.com/