There is no universally acknowledged minimum amount of copper standard for calling a cuprian tourmaline a Paraíba tourmaline. However, here is how the Laboratory Manual Harmonisation Committee (LMHC) defines Paraiba tourmalines:
A paraiba tourmaline is a blue (electric blue, neon blue, violet blue), bluish green to greenish blue, green (or yellowish green) tourmaline, of medium-light to high saturation and tone (relative to this variety of tourmaline), mainly due to the presence of copper (Cu) and manganese (Mn) of whatever geographical origin. The name of the tourmaline variety ‘paraiba’ is derived from the Brazilian locality Paraíba where this gemstone was first mined.
So, by this definition, Cu and Mn must be present in some amount in the tourmaline, along with the specified hue, tone, and saturation.
This GIA article has data on the ranges of Cu and other elements parts per million weight based on a LA-ICP-MS analysis of 301 Paraiba tourmalines from Brazil, Nigeria, and Mozambique. (Table 2). These figures are not intended as Cu standards, but they can serve to give some idea of amounts you can find in these stones. (And could also help determine geographic origin).
Hope this information helps.