A valid question, indeed, why is it called The Falcon and The Winder Soldier and not The Falcon's Captain America and The Winter Soldier considering that Captain America already gave his shield to The Falcon? Anthony Mackie, The Falcon himself, cleared the air on this question by saying that while he is now the holder of the shield of the cap, there was no showing that Sam Wilson agreed or that he would be Captain America. Mackie added that the series will be showing who fills the shoes of Captain America if Steve Rogers would not be coming back.
Recalling Avengers: Endgame, after the fall of the Mad Titan, Captain America took the responsibility of putting all the stones they borrowed in their proper timelines but did not come back as expected. Steve Rogers utilized his time well, indeed, as he decided to stay in the past and reunite with Peggy Carter to finally make it to the dance that he never got the chance with her. Seeing Captain America turn gray and old with a genuine smile on his face, Steve seemed to have the time of his life with his love. But this act of Captain America will surely have its consequences, it can be remembered that in Marvel's Agents of SHIELD, a constant reminder for those traveling back in time is "only make ripples, not waves." With Steve coming back to the past and living out the rest of his life in a different perspective, it could be assumed that he made waves like all the events before his time-travel would be altered, creating a whole new timeline.
The title of the series could also pay homage to a 1985 film The Falcon and the Snowman which tackles the story of a disillusioned CIA agent trading information with the USSR, but that is too early to assume.
With the Falcon currently holding the shield, it is safe to say that he will be carrying the complicated legacy of the shield but it does not automatically make him Captain America in an instant. It could only pave way for his development which could shape him up to be the next Cap. After all, the shield is just a shield until a hero holds it; the shield is just a symbolism of power and responsibility of carrying it, not directly pinpointing who will own it. The hero wears the shield, not the other way around.