The auto-completion recognizes all names in the function list, but only those from the current file. This is not mentioned in the help. It seems, IDM has forgotten it to add this fact to the help after adding the feature of showing all functions of the whole project in the function list.
You can right-click on the function list and copy the list to clipboard. Now open either the wordfile for syntax highlighting and add all function names to a language group (a new group) of the current language set or save the function names to a special auto-complete file. For both versions you need to update the list in the corresponding file manually when you add a new function.
The problem with auto-complete of all function names of all project files is, that the function list normally contains the names of all functions, independent if the function is private or public. So the auto-completion would also show/add functions, which cannot be called from the actual module, because the function is not public in the other module.
Best regards from Austria