At least in Polish Autocephalous Orthodox Church saint Adalbert is not venerated. I had a friend that was a member of PAKP from a mixed (catholic-orthodox) family. His mother wanted to name him "Wojciech", but the parish priest disagreed. So he had the name "Wojciech" written in secular documents but was baptised with name "George" and thus he was known for people from orthodox parish in Poznań.
The possible reason why he is not venerated byt PAKP was his negative attitude towards cirylo-methodian tradition. There is an ancient chronicle which states:
zniszczył wiarę prawdziwą i słowiańskie pismo odrzucił i zaprowadził pismo łacińskie i obrządek łaciński; obrazy wiary prawdziwej popalił, biskupów i księży jednychpozabijał, drugich rozegnał
destroyed the true faith and rejected the slavonic script introducing the latin script and latin rite; the icons of true faith he burned, from the bishops and priests, he killed some and banished the others
I don't know if there are any other reasons that Saint Adalbert is not accepted by PAKP. I never read any official declaration of the Holy Council of PAKP about Saint Adalbert.