try this script:
with open("data.json") as f:
    data = json.load(f)
    data["id"] = 134
    json.dump(data, open("data.json", "w"), indent = 4)
the result is:
{
    "name":"mynamme",
    "id":134
}
Just the arrangement is different, You can solve the problem by converting the "data" type to a list, then arranging it as you wish, then returning it and saving the file, like that:
index_add = 0
with open("data.json") as f:
    data = json.load(f)
    data_li = [[k, v] for k, v in data.items()]
    data_li.insert(index_add, ["id", 134])
    data = {data_li[i][0]:data_li[i][1] for i in range(0, len(data_li))}
    json.dump(data, open("data.json", "w"), indent = 4)
the result is:
{
    "id":134,
    "name":"myname"
}
you can add if condition in order not to repeat the key, just change it, like that:
index_add = 0
n_k = "id"
n_v = 134
with open("data.json") as f:
    data = json.load(f)
    if n_k in data:
        data[n_k] = n_v
    else:
       data_li = [[k, v] for k, v in data.items()]
       data_li.insert(index_add, [n_k, n_v])
       data = {data_li[i][0]:data_li[i][1] for i in range(0, len(data_li))}
    json.dump(data, open("data.json", "w"), indent = 4)