Looking for pinpoint accuracy in a common name is pointless - common names for plants vary from region to region, country to country, which is why you have three common names for the same plant already.
The botanical or Latin name for a plant, in its entirety, is the only way to ever be sure what the plant is, right down to the specific variety or cultivar. Common names for plants are often unhelpful - for instance, in the UK, Bouncing Bet is the common name for a particular plant in the South of the country, but further north, the same plant is referred to as Tumbling Ted. Further, some common names are also applied to as many as three or more entirely different, unrelated plants.
Essentially, if plants are referred to by their common names only, no one ever really knows exactly which plant is meant - in theory, you could call a plant Fred Jones and if you said it often enough to as many people as possible, that name, over time, would become accepted as the plant's name in your locality. Personally, I feel strongly about the use of common names; I find them incredibly irritating because they're unclear and confusing. It's rather like having a conversation with someone who's talking about Tom's behaviour, and eventually you realise they're referring to their pet lizard, not their partner.
There may well be other common names for Beaumontia, but clearly, the three you already have are the most well known ones.