Yes, this algorithm has a name. It is called binary search. Here is a Python code that implements binary search:

```python
def binary_search(arr, target):
    low = 0
    high = len(arr) - 1

    while low <= high:
        mid = (low + high) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            low = mid + 1
        else:
            high = mid - 1

    return -1
```

This function takes an ordered list (arr) and a target value as input and returns the position of the target value in the list if it is found, or -1 if it is not found.