Using Windows as an example here.
Download the Opera installer, launch it, click "options", set "install path" to "C:\Users\yourusername\My Program Files\Opera Business", set "install for" to "Standalone Installation" and install.
Right-click on "C:\Users\yourusername\My Program Files\Opera Business\launcher.exe" and create a shortcut to it. Put the shortcut where you want and rename it to "Opera Business".
Right-click on the shortcut and choose "properties". Then, on the "shortcut" tab, modify the value of the "target" field to be:
"C:\Users\yourusername\My Program Files\Opera Business\launcher.exe" --private
Repeat all those steps for "Opera Shopping" and "Opera Personal". Skip modifying the shortcut tab if you don't want to start with a private window.
For each of those, you can adjust the settings for what to accept and retain as far as cookies etc. go.
There's also another way to do it instead.
Just create multiple shortcuts to "C:\Program Files\Opera\launcher.exe", name each what you want and modify their targets like so:
"C:\Program Files\Opera\launcher.exe" "--user-data-dir=C:\Users\youusername\AppData\Roaming\Opera Software\Opera Business" --private
"C:\Program Files\Opera\launcher.exe" "--user-data-dir=C:\Users\youusername\AppData\Roaming\Opera Software\Opera Personal" --private
"C:\Program Files\Opera\launcher.exe" "--user-data-dir=C:\Users\youusername\AppData\Roaming\Opera Software\Opera Shopping" --private
Again, skip the "--private" if you don't want it and use any path in your userprofile space you like for the user data directory. The default Opera profile will be in "Opera Software\Opera Stable" that gets used when you don't launch Opera with one of those specific shortcuts.