```python
def row_key(name: str) -> str:
    """Return the first letter of a name in upper case."""
    if not name or not isinstance(name, str):
        raise ValueError("Input must be a non-empty string.")
    return name[0].upper()

def index_rows(names: list) -> dict:
    """Return a dictionary where keys are the row keys and values are lists of names."""
    if not names or not isinstance(names, list):
        raise ValueError("Input must be a non-empty list.")
    result = {}
    for name in names:
        key = row_key(name)
        if key not in result:
            result[key] = []
        result[key].append(name)
    return result
```