Path.GetFileNameWithoutExtension(string)

Description

Returns the file base component of the specified path string without the extension.

The return value consists of the string returned by GetFileName(), minus the extension separator character and extension.

using System.IO;
using UnityEngine;
using System.Collections;

public class ExampleClass : MonoBehaviour {
    void Start() {
        Debug.Log(Path.GetFileNameWithoutExtension("/Some/File/At/foo.extension"));
    }
}