I know there have been other responses - but I'd already typed this out before there were, so...
If LA has accepted your BAEC membership number, despite the slight name mis-match, then the flights should credit automatically.
If LA does not have your BAEC number, then the flights will not track, they won't know you're BA Gold/OWE, and you'll have to retro claim you Avios/TPs from BA (not Orbitz). If it's really important to you for LA to have your FQTV up front, you'll need to have Orbitz process the name correction, which may or may not be possible, depending on LA's policies.
Sabre does accept spaces in names (I just worked a booking with one) - but it might be that Orbitz, (or the system Orbitz use if it's not Sabre) automatically remove any spaces entered. Ideally, spaces shouldn't be entered anyway, as it can possibly confuse some inter-airline systems. I realise autocomplete got you here, but if you were typing your own name in, it's best practice to type 'JOHNNY' or 'JOHNNYCORNELIUS' but to avoid 'JOHNNY CORNELIUS' or 'JOHNNY C' while 'JOHNNYC' is acceptable but not great.