Hi, I found a post online by Sally Dorans suggesting the Vann and Vans families may be related. Since I can't post on GenesReunited without paying, I'm posting it here in the hopes that she'll see it,
Hi Sally, It's an interesting question! - and as you can imagine, I don't know the answer. My own feeling is that any Vanns in England who are related to the Vans's of Dirleton and then Barnbarroch, if there are any, are probably related from the time immediately after the Norman conquest, and before they got to Scotland; from their English phase, you might say. But there are quite a lot of C17 and C18 Vans's unaccounted for, any one of whom could have ended up in England (some did, in London, for example Archibald Vaus, b 1678, a card maker in London). I see no conclusive reason why Vans shouldn't become Vann, except that in Scotland, the 'a' sound is long, so it tends to be pronounced 'Varns'.
So, I dunno, I'm afraid. Unless you can find a picture of the Vann arms - then it's easy to see whether it derives from Vans, and perhaps at what date to. Try the College of Heralds.
Regards, Jamie Vans. Email me at jvans (at) dsl.pipex.com if you like.