Visited on 21st April - this one's tricky! Found two signs, both on buildings. One is an old plaque, black text on white=painted metal, reading "WATCH BELL SṬ". The other is black text painted onto a short row of white-painted bricks, and reads "WATCHBELL STREET". No modern council street name sign found.

Most sources (examples follow) use "Watchbell", so I suggest using this and having an alt_name of "Watch Bell Street".

https://ryemuseum.co.uk/watchbell-street/
https://historicengland.org.uk/listing/the-list/list-entry/1252063
https://historicengland.org.uk/listing/the-list/list-entry/1252058