Dyson V8 (star pre-filter) filters and battery
A 965661-05 pre-motor filter, a 967478-05 post-motor filter and a 974815-01 battery.
Every version in the "Also covers" list takes the same parts.
Pre-motor filters
Post-motor filters
Batteries
Finding the model number
It's worth a look at the rating plate first, because names get reused across generations. Serial number on the bottom of the machine (battery and charger have their own).
When to change them
Washable filters go back in bone dry or not at all. A damp one smells, and on some machines it can let the motor pull moisture through.
A battery doesn't die overnight. The run time on a full charge shrinks month by month, and once it won't get you round the house it's time for a new one.
If it cuts out with charge left, look for a blockage in the wand or filter before you blame the battery. A clogged machine can stop just like a flat one.
Quick answers
What pre-motor filters does the Dyson V8 (star pre-filter) take?
965661-05, sold by Dyson as the Dyson pre-filter 965661-05 (V8 with star pre-filter).
Which post-motor filters fit the Dyson V8 (star pre-filter)?
967478-05, sold by Dyson as the Dyson post filter 967478-05 (V7 / V8).
Buying for a Dyson V8 (star pre-filter), which batteries should I get?
974815-01, sold by Dyson as the Dyson V8 battery 974815-01.