Create a new desktop icon in ~/.local/share/applications.

Use this as a template

[Desktop Action new-private-window]
Exec=chromium-browser --incognito
Name=New Incognito Window

[Desktop Action new-window]
Exec=chromium-browser
Name=New Window

[Desktop Entry]
Actions=new-window;new-private-window;
Categories=Network;WebBrowser;
Comment[en_US]=Access the Internet
Comment=Access the Internet
Exec=chromium-browser --user-data-dir=/home/akujin/.config/chromium-ihub/ --app-id=iHubChromium --class=iHubChromium && xdotool search --sync --classname iHubChromium set_window --class iHubChromium
GenericName[en_US]=Web Browser
GenericName=Web Browser
Icon=/home/akujin/iHub/logo-square.png
MimeType=text/html;image/webp;image/png;image/jpeg;image/gif;application/xml;application/xml;application/xhtml+xml;application/rss+xml;application/rdf+xml;application/pdf;
Name[en_US]=Chromium iHub
Name=Chromium iHub
Path=
StartupNotify=true
StartupWMClass=iHubChromium
Terminal=false
TerminalOptions=
Type=Application
Version=1.0
X-DBUS-ServiceName=
X-DBUS-StartupType=
X-KDE-SubstituteUID=false
X-KDE-Username=

Run update-desktop-database ~/.local/share/applications after any changes to the desktop file.

And there you have it. A custom icon.