That sounds like a Hammer Curl as per the list here.
This bicep curl variation is like the standard biceps curl with one small adjustment. Turn the palms towards the midline of the body with the thumbs up. Curl the weight up towards the shoulder creating flexion only at the elbow. Extend the elbow and lower the weight back to the starting position.
The rotation of the palms adds a focus on the brachialis and brachioradialis in a way that many other variations cannot.
How-To Video
Adding the elbow floating away turns it into a "cheat curl" variation. Here, the "cheat" is not necessarily meant pejoratively. It just means that, by letting the elbow move, you're recruiting other muscles, such as the deltoids in your back, which reduces the biceps isolation, but will allow you to lift more weight, which can translate to a bump in your ability to lift heavier weight in a "strict" hammer curl.