Among 'athletic pants', 'sport pants', 'workout pants', which is the most common name used in AmE?
There are a number of words used for this type of clothing.
Athletic pants would be understood, but it sounds more like the type of term used by clothing manufacturers to describe this category of clothing. You wouldn't normally hear two people at a gym describing their pants to one another with this phrase.
Workout pants would be usable for any sort of pants of this type. People are more specific about what they are wearing usually, but if you said something like:
Give me a minute to change into my workout pants before we leave for the gym.
it would be perfectly normal. Workout pants can also refer to a variety of uncategorized pants or be used for pants whose category is unknown.
Loose fitting cotton or polyester pants like the ones shown below are commonly called sweat pants (or sometimes sweatpants.)
If the pants are lightweight and nylon, they are often called warm up pants, and can be part of a tracksuit. If they have snaps down the sides they are tear away pants. Both varieties are sometimes called basketball pants. The woman below is wearing a tracksuit, a matching pair of warmup pants and jacket.
Finally, there are form fitting pants that have become popular with women in the US in the past few years that are called yoga pants. They are very similar to sweat pants, but are usually much tighter fitting. Be aware that searching for images of yoga pants will probably not be safe for work.
All images were cropped and resized.