Модель:
public class CinimateListModel
{
[JsonProperty("name")]
[JsonConverter(typeof(BadListsJsonConverter<string>))]
public List<string> Names { get; set; }
}

Кастомный конвертер
public class BadListsJsonConverter<T>:JsonConverter
{
public override void WriteJson(JsonWriter writer, object value, JsonSerializer serializer)
{
throw new NotImplementedException();
}

public override object ReadJson(JsonReader reader, Type objectType, object existingValue, JsonSerializer serializer)
{
var retVal = new Object();
if (reader.TokenType == JsonToken.StartArray)
{
retVal = serializer.Deserialize(reader, objectType);
}
else
{
var instance = (T)serializer.Deserialize(reader, typeof(T));
retVal = new List<T>() { instance };
}
return retVal;
}

public override bool CanConvert(Type objectType)
{
return false;
}
}