If you have a greenscreen, you can simply remove the background with a chromakey and insert a logo-wall graphic on the layer below your webcam which will fill in the transparency, then use a horizontal flip to put the camera into 'mirror' mode, unless you're wearing a shirt/hat/tie/etc with text on it (which will show as reversed).
Otherwise... this is a pretty standard thing. It's camera- or stage-direction.
Just as when you're facing a live class, if you raise your right hand and gesture to your right, for anyone looking at you, you'll have raised the hand on and gestured to their left. It's simply an adjustment to make and remember, if you're working with composited-in assets rather than physical props. There's definitely an adjustment period.
It isn't like looking in a mirror, where when you raise your right hand, the hand on the right in the reflection (which would be the reflection's left hand) goes up. It's totally normal, and trips everyone up when they first start seeing their own blocking from the audience's point of view in the preview. Just a skill to learn and become proficient in.
It CAN help to put a couple of post-its on either side of your camera though, when you're first practicing it, with RIGHT on the left side, and LEFT on the right side, with arrows. Just as a quick reminder for yourself, until it becomes second nature. Likewise, to spend 15 minutes every few hours or so coming back and practicing it, when you aren't doing a live presentation.