The name came from a previous exploit called BlueKeep, which wasn't related to BSOD.

In fact: "On 6 September 2019, an exploit of the wormable BlueKeep security vulnerability was announced to have been released into the public realm.[4] The initial version of this exploit was, however, unreliable, being known to cause "blue screen of death" (BSOD) errors. A fix was later announced, removing the cause of the BSOD error."

They even fixed a BSOD issue that popped up in BlueKeep as that was no good to them.