Considering how low key Luciano and his faction were I'm sure they were just fine with the family going by "Genovese". Lucky probably hated his name attached to it in the first place. Wasn't his style.

"...the successful annihilation of organized crime's subculture in America would rock the 'legitimate' world's foundation, which would ultimately force fundamental social changes and redistributions of wealth and power in this country. Meyer Lansky's dream was to bond the two worlds together so that one could not survive without the other." - Dan E. Moldea