I'm upgrading my crappy 2013 prebuilt PC to a nice one. I'm switching the motherboard, the CPU, the GPU, the PSU, new OS, the Case, and adding a CPU cooler. If I build this, would the "HP" be removed off of my BIOS and OS?
Well if you're switching the motherboard, it won't show HP anymore. The logos are locked with the brand of the Motherboard.
For example: Buy a Asus motherboard, boot will show Asus. Buy MSI..boot will show MSI.