I don't think that "Ace and Aro" implies both, as it is. I think the logo definitely needs work, but, as you said, that takes know-how and time, so doing your best to make it as obvious as possible that it's both is good. I'm in agreement that "Liverpool Area Ace and Aro Group" is pretty generally a good and used format in many areas.
The biggest thing is the language change - changing the group name to "Ace and Aro", changing the language used in discussions to "a-spec"...these are all things that need to be done that don't require as much effort, but are important to overall inclusiveness.
As much as this suggestion is well intentioned, this isn't practical or...what they were asking? No offense at all, @Mark, but this comes across super unfriendly to the concept of allowing a group to grow to be inclusive, even if it wasn't originally. The group is currently alienating even to me if the group is called "Liverpool Aces Meetup" or something along those, because I identify more with my aro-ness. However, that suggestion is not helpful or practical, unless you're in the Liverpool area and want to start a group yourself.