How can I parse a JSON string that would cause illegal C# identifiers?

You can deserialize to a dictionary.

public class Item
{
    public string fajr { get; set; }
    public string sunrise { get; set; }
    public string zuhr { get; set; }
    public string asr { get; set; }
    public string maghrib { get; set; }
    public string isha { get; set; }
}

var dict = JsonConvert.DeserializeObject<Dictionary<string, Item>>(json);

While the dictionary is the best solution for the specific case you had, the question you asked could also be interpreted as:

how do I deserialize objects with property names that cannot be used in C#?

For example what if you had

{
    "0": "04:15",
    "zzz": "foo"
}

Solution: use annotations:

public class Item
{
   [JsonProperty("0")]
   public string AnyName { get; set; }

   [JsonProperty("zzz")]
   public string AnotherName { get; set; }
}