If you saw the bug on the 6 News Now intro, the Fox logo remains in the station’s logo alongside the revived ABC-era “6”. So, unless they plan to keep the network logo but deemphasize the “Fox” branding verbally or modify the logo to remove the Fox logo once the package officially launches, it seems like the “WBRC Fox 6” brand will remain in place.
WVUE and WALA have kept their Fox branding after switching to the package; to date, Gray stations that have dropped network branding have usually made the change before (like with WMTV and KOSA) or when they switched to GrayONE. Fox has stricter branding guidelines than other networks, and has been pretty selective in allowing affiliates to eschew network references (like it did with WSVN, WDRB, KVRR, WFXT and, before Fox bought it and to a lesser degree, KTVU), so it’s unclear whether Gray will be given the same license to deemphasize network branding.