A thought about Dave's name

So in DSaF 3 you can buy the filing cabinets that include logs made by Henry talking about his plans and how he uses Dave as his test subject, ect. So in one of them Henry talks about he told William about his dead son "David" and how William tries and acts like a son and treat Henry as the father he never had. He talks about leaving William n stuff as he's not changed after removing his vital organs. Soooo what I'm try to get at is what if William took the name Dave, can also be called David sometimes, because he really wanted to be Henry's dead son. Anyways I played this game for 10 hours straight so I might have heard the logs wrong, but that us what I think.

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-Update-

In DSaF 3 during the bad run. William tells you his real name and how Dave Miller is the person he wishes to be. So I have concluded William took the name of Henry's dead son.