If the President doesn't name a candidate to fill a Supreme Court vacancy, can the Senate fill the seat, anyway?
If Biden were to win re-election, the Republicans take the Senate, and a Supreme Court vacancy occurs, a Republican Senate would never confirm any Biden candidate, if for no other reason than pure spite.
The Constitution allows a President to not name a candidate. This would create an 8-member, 5-3 Republican SCOTUS, which is better than a 6-3 Republican majority. If one Republican votes with the Dems, you have a tie and no change from the status quo.
In this scenario, I don't think that the Senate could appoint a candidate, hold a confirmation hearing and fill the vacancy.