Anonymous recording of any video you transmit is blindingly easy for any viewer, so a better route is to think about what you can control.
You are probably better off watermarking the image with a “do not record” and add a DCMA mention for good measure. This makes it easier to threaten legal action to order whatever host site the video is on. Another trick might be to anonymize the transmission so only the body is showing, no face, or vice versa, the face is showing but not the body. Controlling the quality is another route. So if you restrict the outgoing resolution by using a crappy streaming app with a poor connection, that reduces the quality of any recorded video on their end.
Using predominantly mobile apps will reduce the likelihood of recording, since most devices that are intended for streaming video only, they don’t have built-in record functions, and another separate recording app in the background is usually not possible for most non-tech savvy users. Predominantly streaming mobile apps such as Skype, Viber, FaceTime, WeChat, that don’t have inline recording options could be good choices. These all have desktop equivalents of course; which means another recording app can be run in the background to silently record.
Teleconferencing apps that have their own built-in recording features such as Zoom or WebEx that politely put a “record” indicator to let the broadcaster know the video is being recorded, but again, that is easily defeated by using a background screen capture app to do a screen recording.
Also, pick an app that is bi-directional so their image is displayed to you while your image is transmitting. This at least gives you more ammunition to use the person’s face as a deterrent should they misuse your image.