If you are using JMP 14, you can use File->Multiple File Import. MFI uses a directory and a file name pattern. The file name pattern can be the actual file name. Check the box to change the pattern. In your case, you'll only select a single file, so the Stack Similar Files choice won't make a difference. You won't need the Select files by size or by date and time filters either. On the right, you can see the number of files available after each filter is applied.
You can add the File Name column or use the table name or use the Files table variable. The Source table variable contains the JSL to run the import again.
If multiple files were stacked, that list would be longer. For example,
fileList = dt<<getTableVariable("Files");
show(fileList);
fileList = "{{\!"gpsLog3.txt\!", 1, 354331}, {\!"gpslog.txt\!", 354332, 71551}}";
means the gpsLog3 file starts on row 1 and has 354331 rows and the gpslog.txt file starts on row 354332 and has 71551 rows.
Craige