First, from your BPM Invites (aka Captain's List) page, click the "Change" button in the top right corner.
Then, you will see two options. The first is specific BPM which is what you usually see by default. It shows just the names from the one specific BPM you have selected. But, if you click "Date Range" you can then select a date range that you want to get all your names for. This will list out all names for all BPMs that you had during the selected date range.
You should then see a list of all your names on screen with a new column that shows which BPM they were invited to. It may take a bit to load if there are lots of names. Last, if you want to export those names, just click the printer icon at the bottom left of the table and select the format you want to export to.