Thank you! Yes, the custom blocks themselves (the 'Content' field) are multilingual. But the 'Block Name' field is not multilingual, and it is not displayed.
Whereas the standard blocks' names are displayed and they are multilingual. So if I have English-French journal, I would get 'Language' name displayed for the Language toggle block in the English version and 'Langue' in the French.
When the user creates his/her custom block, (s)he expects the block name to be displayed and be multilingual, just as it is in the standard blocks. So I would add 'make a proper title field multilingual' to the request, if that is possible.