I'm looking for a screencast software that can record my screen and my face (using my webcam) in a Picture-in-picture (you know, that secondary video in a small rectangle in the corner of the screen).
Ubuntu – Is there an app for screen recoding with PIP (picture in picture)
screencastsoftware-recommendation
Related Solutions
gtk-recordmydesktop 
Adds an easy to use graphical icon on the GNOME toolbar to make a pleasure use and configure the audio and video capture and screencast application recordMyDesktop.
As mentioned at 20.04: Can't install gtk-recordmydesktop and on the package search, the package is not available on the main repository anymore, and sudo apt install gtk-recordmydesktop fails. I'm not sure why the http://apt.ubuntu.com/p/gtk-recordmydesktop link seems to work, maybe it installs an older version. But this indicates that the software is not being actively supported.
recordmydesktop
This is the non-GUI backend of recordmydesktop, and it is still available in 20.04:
sudo apt install recordmydesktop
recordmydesktop --on-the-fly-encoding
This will record until you stop the program on the terminal e.g. with Ctrl + C.
--on-the-fly-encoding encodes the output immediately; without it you need to wait for a possibly long time at the end for the encoding to be done. I haven't seen any significant downsides to that option yet, likely it will just take a bit more of CPU resources, but it is generally worth it.
It should be able to do everything that gtk-recordmydesktop does, but it is a bit harder to learn as you have to deal with the command lines.
You can set a stop recording shortcut e.g. with:
recordmydesktop --stop-shortcut=Control+s
You can select to record a single window as shown at: How can I get the value of Window ID?
recordmydesktop --windowid `xwininfo | grep 'id: 0x' | grep -Eo '0x[a-z0-9]+'`
This will allow you to first select the window with a mouse click, and it starts recording after you click.
How to record sound output with it: https://unix.stackexchange.com/questions/3490/how-can-i-record-the-sound-output-with-gtk-recordmydesktop
xvidcap (no longer maintained, package is no longer available)
A screen capture enabling you to capture videos off your X-Window desktop for illustration or documentation purposes. It is intended to be a standards-based alternative to tools like Lotus ScreenCam.
Video can be saved in MPEG or AVI files format.
kdenlive 
Kdenlive is a free open-source video editor for GNU/Linux and FreeBSD, which supports DV, AVCHD and HDV editing. Kdenlive relies on several other open source projects, such as FFmpeg, the MLT video framework and Frei0r effects.
Kdenlive is easily the best video editor currently available for Ubuntu. There is also a GTK frontend for MLT framework (OpenShot) but it has less features and worse user interface.
Kdenlive supports a wide array of video formats, images and transitions. The rendering tool has ready presets for most situations like Youtube, DVD, different mobile devices, etc. so you don't need to be an expert on video compression.
You can get it from Ubuntu's repository, but I'd suggest you get the latest version from project site. They even have a repository set up for Ubuntu.
Best Answer
You can use webcam studio.
Some of the features include:
Download from here
source
Another way is to use the Gnome Mplayer
you can install by:
This command will show the window of the webcam output while screencasting so any screencast software you can use can also screencast your webcam output so you don't need other software to merge.
Please watch this video to demonstarte how to use gnome-mplayer in screencasting with webcam window enabled
How to record my screen? : List of screencast software for Ubuntu( Personally I advise you kazam)