Name necklaces are easier than ever to find online, especially thanks to Sex & The City. Janet's script necklace connects to the chain at the 'J' and 't'. The chain is probably about 16" - 18".
Janet's 'J' doesn't have any sharp corners - it's rounded at the top and bottom.
Updated 9/9/21: At this point, you should be able to find something on Etsy - so I removed the outdated links to Sears