My Doom Unity port has German language selected by default (I am using a German system), but I would like to switch to English. However, I cannot find any menu entry for that.

Is there even a way to do this in the GOG.com release? Maybe there is a launch parameter or something?

You have to select the language before installing the game when using the offline installer files (see screenshot).
To find language options in GOG Galaxy go to Manage installation > Configure > Installation.

I tried reinstalling with the offline installer and made sure I had selected "English" as language in both the popup window in the beginning and the installer window later on. However, I am still only getting German ingame language afterwards.

That's weird it should work just fine.
One more thing you could try is opening the goggame-2015545325.info file inside the game folder with a text editor and check if all the language parts inside are set to English.

The info from that GOG file you posted above proved to be useful. When using "--bnet-language de" as a command line parameter during game startup (e.g. "DOOM.exe --bnet-language de"), everything will be in German and also stays like that if the parameter is removed afterwards. Launching with "--bnet-language en" (e.g. "DOOM.exe --bnet-language en") switches the game to English permanently.

What this actually does is to change registry key "I2 Language_h3293684300" for Doom 1+2 in
- HKEY_CURRENT_USER\SOFTWARE\Bethesda Softworks\DOOM
- HKEY_CURRENT_USER\SOFTWARE\Bethesda Softworks\DOOM 2

Instead of using that --bnet-language parameter, you could also create and execute a .reg file with this exact code inside:

Windows Registry Editor Version 5.00

[HKEY_CURRENT_USER\SOFTWARE\Bethesda Softworks\DOOM]
"I2 Language_h3293684300"=hex:45,6e,67,6c,69,73,68,00

[HKEY_CURRENT_USER\SOFTWARE\Bethesda Softworks\DOOM 2]
"I2 Language_h3293684300"=hex:45,6e,67,6c,69,73,68,00

It will switch both your games to English permanently. (The hex code for German would be "47,65,72,6d,61,6e,00", btw.) This confirms my assumption that it's not a matter of installing different files during setup, but flipping an internal switch to make the game use the desired localization assets.

Side note:
Installing this via GOG Galaxy sets the loca flags properly as well, but for some reason it won't with the offline installers, at least for me.