Siwan

Just about all the pronunciations in the comments here are wrong.
Starting at the beginning, in Welsh Si is a digraph that represents the English sh sound (an unvoiced fricative) but it is also true that that in Welsh iw is, effectively, a diphthong whose English equivalent is the ew in the English "grew".
Obviously, since Siwan is the Welsh rendition of Joan, Si as a digraph takes precedence over considering iw as a diphthong because, there being no letter J in Welsh its sound is always approximated by the use of si.
All this would lead one to think that the common pronunciation in Wales of Siwan should be Shoo-an (the letter "a" is NEVER ever pronounced as "u") but it is an awkward fact that in Wales it is most commonly pronounced Shewan (English orthography) even amongst Welsh speakers from Welsh speaking families, people like me. My own daughter was Christened Siwan and that is how she and the rest of the family pronounce it. In terms of its voicing it more closely resembles Joanne than it does Joan.

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No disrespect, Madison but Siwan could only be pronounced See-wan if the I was accompanied by a "to bach" (circumflex) to signal that it stands as a separate letter and that it neither combines with the preceding S as part of a digraph nor with the following W to form a diphthong.

Both pronunciations are correct. First-language Welsh speakers pronounce it either 'shew-awn' or 'siew-awn'.

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'Si' is pronounced 'shhh' before a vowel and 'si' before a consonant but the letter 'w' functions as a vowel or a consonant depending on the situation. First-language Welsh speakers will use either pronunciation depending on their dialect.

It is a very beautiful name. However the correct way to pronounce it is Shee-oohanne. It is my sister's name and many people pronounce it wrong as See-oohanne. The traditional and correct way of saying it is with a Sh.

Here is a link to how it's pronounced:

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http://www.bbc.co.uk/wales/colinandcumberland/south/littleblackbook/wordbank/introducing_yourself.shtml

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It sounds like seew-ann or see-oo-ann.

It's actually pronounced Seew-Anne, or that's how my history teachers pronounce it. Llywelyn The Great had a daughter or a sister or a wife called this.