Which name should I use for filing the application?

[Terpe]

I took mine last February and the expiration date is in august. So it looks like, the validity is just for 6 months

Yep, spot on
The TB Certificate is valid for 6 months from the date that it is issued.

JenBoo, for UKVI information on TB screening in the Philippines take a look here

and for some really detailed information on all aspects of TB Screening also take a look here