I have no idea why you think the name helps remove the need for a visualization. Besides I think "filter" is more apt than "table"—it doesn't store anything per se.
I never needed a picture to understand a hash table once I knew what a hash function was. If it were called a McCready table, that's one more trip to Wikipedia, plus one more every time I forget.
Re: naming: It's a table of hash function results. It probabilistically stores a set. I don't see any filter here, though one use of the technique is indeed in filtering a list, though there are plenty more.
Right, but you're describing the implementation, which doesn't imply anything about its use. I prefer to name by the latter: the implemenation is just a detail on how the filter does its filtering.
Re: naming: It's a table of hash function results. It probabilistically stores a set. I don't see any filter here, though one use of the technique is indeed in filtering a list, though there are plenty more.