I'm not sure how you could possibly anglicize that, short of adopting an entirely new name. "Sean" would be phonetically close, but Siobhan is exclusively feminine.
Anecdotally, I've never met a "Shavaun" (or "Chivonne", etc).
All the "Siobhans" I've met seemed proud of their Irish heritage and history. Making it easier and losing the Gaelic "bh" seems a bit more lower-class.
>"I've never met a "Shavaun" (or "Chivonne", etc)."
I wouldn't think I could say the same. My work means I do spell the names of most people I meet, but certainly not all. I consider my spelling to be very good but even so there are names each week that I can't spell [correctly] and/or have never written before. Homophonic alternative spellings appear to be in vogue.
As it happens I knew someone for maybe 20 years called Siobhan before I learnt that was how you spelt it; if she was using a alternative spelling I'd never have known.
It seems like there'd be a selection bias, and our cultural attitudes toward outsiders have shifted various directions over time - we're currently pretty accepting of the Irish.
Slightly off-topic: I can't find a link, but I'm sure I read somewhere that Irish speakers in the nineteenth century would routinely anglicise their own names when writing in English: e.g., a man called Sean would sign letters as "John".
I'm not sure how you could possibly anglicize that, short of adopting an entirely new name. "Sean" would be phonetically close, but Siobhan is exclusively feminine.