I think you'll need to grow that little plant out to see what the flowers look like before an ID will be likely.
Don't think Basil could cross with Oregano anyway, but if they did, the most common way is by cross-pollination which requires the flowers to bloom, produce seeds, then the seeds to germinate. This little plant grew from a seed, right? There might be another variety of Basil in with the seeds you got. Or a sport.
