In my opinion GP batteries regardless of whether rechargeable or non-rechargeable type, are lousy. And the GP non-rechargeable type tend to leak which destroys your expensive flash equipment with corrosive chemicals. Although GP may have improved over the years, I do not wish to take the risk again.
Eneloop rechargeable batteries seem alright. I have tried the Ikea rechargeable batteries but personal preference is for Eneloop. There are two types. White and Black. The black Eneloop is the Eneloop Pro that cost more. Since your flash is a Sony flash, why did you not take a look at Sony Rechargeable batteries?
If price is not a problem, you can consider Lithium AAA batteries (they are non-rechargeable) for your flash. Energizer is one of the brands.