In England and Wales the centre has said Poppy Fund for a while now. In Scotland it still says Haig Fund.(At least it did last year. Not been north of the border this year.) Scottish poppies also have four petals as opposed to the normal two. All the money goes to the same place, the RBL.
The white poppy money just goes to making more white poppies.
The current Earl Haig is a poppy seller ,"some where in England" and has no objection to the name change.