Unfortunately MySQL does not feature a split string function. However you can create a user defined function for this, such as the one described in the following article:
With that function, you would be able to build your query as follows:
SELECT SPLIT_STR(membername, ' ', 1) as memberfirst,
SPLIT_STR(membername, ' ', 2) as memberlast
FROM users;
If you prefer not to use a user defined function and you do not mind the query to be a bit more verbose, you can also do the following:
SELECT SUBSTRING_INDEX(SUBSTRING_INDEX(membername, ' ', 1), ' ', -1) as memberfirst,
SUBSTRING_INDEX(SUBSTRING_INDEX(membername, ' ', 2), ' ', -1) as memberlast
FROM users;