If the functionality isn’t that different between them, sure it makes sense. If they are different and you need to actually generate public documentation for them, then you will probably need to break out into separate functions you can document.

def handle_event("widget_fizzled", params, socket), do: handle_widget_fizzled(params, socket)
def handle_event("fizzerator_gringled", params, socket), do: handle_fizzerator_gringled(params, socket)

@doc """
Handles the case when the widget was fizzled.
"""
def handle_widget_fizzled(_params, socket) do
  # ...
  {:noreply, socket}
end

@doc """
Handles the case when the fizzerator was gringled.
"""
def handle_fizzerator_gringled(_params, socket)
  # ...
  {:noreply, socket}
end

I see this pattern a lot in Erlang libraries - that is the handle*/[*] functions do very little inside the function body and actually just call out another function in the module. Then documentation can be provided on those functions instead.