Automatically sorting in to alphabetical order

In cells A6:O39 I want to sort the rows in to alphabetical order according to the names in column A6:A39.

I can't just set A6:A39 to alphabetical order as there is conditional formatting dotted around, so I need those cells to stay level with the name they are already with.

The spreadsheet is a register. When I add a new name to the bottom I would like it to automatically move it in to it's correct alphabetical position.

I've attached a spreadsheet to help describe what I mean.

I hope someone can help,

Thanks,

Neil.