Two software manager?

Upon upgrading to 20.04, there are apparently two different Software managers. One of them doesn't even have a proper icon

One is called Software, the other Ubuntu Software. I guess this is not what expected?

Two software centers

You have Gnome software center (gnome-software-center) that was already on your system, and has now been upgraded, and the Ubuntu Snap store, a Canonical customized software center installed as a snap, not existing in the the previous LTS release of Ubuntu.

Resolution: Keep both, or remove one of them: sudo apt remove gnome-software to remove Gnome Software, or snap remove snap-store to remove Snap Store.

Lacking icon

The icon issue may be caused because you are using the Humanity icon theme, which remains in effect after the upgrade. The new default icon theme in 20.04, however, is Yaru. It contains a new icon for Ubuntu Software (the snap package), "ubuntusoftware.png", an icon not included in the Humanity icon theme.

Resolution: In case you removed Gnome Software, Snap Store will remain without an icon. Find ubuntusoftware.png of the Yaru theme installed under the /usr/share/themes/Yaru directory and copy or symlink it it to /usr/local/share/icons (or ~/.local/share/icons) for it to become available under your current theme. You may need to create these directories first. Alternatively, you may want to change to the Yaru theme.