LateNightTone
Not quite. There are historical signs for a former establishment, "The Linen Hall" at the eastern end of this building. But the linen hall, after which the nearby streets (and this former pub) are named, was on the site of what is now City Hall (demolished at end of 19th century). Additionally, there is a modern office block a few yards away called The Linenhall, in Linenhall Street, which is already mapped. So to clarify, the specified building is/was not named the linen hall, only a former pub within part of it.

I've added a datapoint to denote the former establishment, only because the signage is still present (and added a note to it). It won't show up in the openstreetmap.org visible layer, but may reduce confusion for future mappers.