I've never heard the name used, but Google comes up with 'nursery web spider' which is quite appropriate. Few spider species have English names, arachnophiles learn binomials Alan
we have a nursery-web spider in NZ too, Dolomedes minor, which even looks similar. T.E.R:R.A.I.N - Taranaki Educational Resource: Research, Analysis and Information Network - Nursery spider (Dolomedes minor) EDIT: well that's why they look similar...Dolomedes and Pisaura are closely related to each other (family Pisauridae).
We have 2 species of Dolomedes in the UK, which are also found in Europe. They live in wet habitats and can walk across water surfaces, so we call them raft spiders. UK zoos are collaborating in a captive breeding program for the fen raft spider Dolomedes plantarius. Pisaura is related but lives in dry habitats. Alan
in NZ we have four species of Pisauridae, three on the mainland and one on the Chathams, and all are endemic. Of the mainland species, one is the nursery-web spider (which usually builds its nest in matagouri or gorse) and the other two are water spiders. All the NZ species are in the genus Dolomedes.