Usually the rule is to remove the added space, if it has obviously not been done to divide the name into two separate words, but if it is a "Mc" or "Mac" name such as Mc Donald , or an "O" name like "O Neil" then we leave the space in.
Sometimes you find that a load of spaces have been inserted into a name to make it fill a box or a line, e.g.
S m i t h
and we have been told in the past not to key those spaces.
But if it is a place name like Blackpool which we are used to seeing as one word, and had been written or typed as Black Pool, we would key the space.