>> +(defcustom imenu-flatten nil
>> +  "If non-nil, popup the completion buffer with a flattened menu.
>> +The string from `imenu-level-separator' is used to separate names of
>> +nested levels while flattening nested indexes with name concatenation."
>> +  :type 'boolean
>
> Here is another useful value for `imenu-flatten' that
> will show section names as a suffix instead of a prefix:

Here is the final patch that adds an option to group Imenu completions.