Your fund size remains $10 million, as that is your target fund size. The $1 million represents the amount you have closed so far, but it does not change the overall target fund size.
The amount of capital that you close on is your fund size, not your target. In other words, if you have a fund target of $10m and you do a 1st close on $1m, your fund size is $1m until you close on more capital.