It's so difficult to have this kind of conversation in written form when we can't hear what people's accents sound like!
In my accent (I'm from the home counties) I would use what I call a short A to describe the vowel sound in words like "van" or "can", and I don't think there's much regional variation in how that sound is pronounced.
The issue is the fact that people who speak like me use what I call a long A to pronounce different words, like "bath" or "castle". So I would say "bah-th"/"bar-th", or "cah-sle"/"car-sle" (depending on how you want to write it), and for me that is a completely different vowel sound to "van" or "can".
When I write "Sharn", I put the R in to indicate that it is the long A sound like "bath" or "castle" or "car" or "harm" or "yarn", which are all the same vowel sound. I don't pronounce it with an R in it, any more than I would pronounce the R in "harm" or "yarn".
I suspect the people saying, "No, it's Shan, like can or van" also say "bath" and "castle" with the short vowel sound.
Would everyone except the people who think it's See Ann or Sigh Ann agree that the vowel sound in Sian is the same as the A in "bath" or "castle"?
If so, that would explain the confusion. 