That's almost what I said. To make it clear
1) The POST runs from the motherboard and displays an image stored on your motherboard. If that's where the HP logo comes from , you are stuck with it. Two tests: One, if you know BIOS well enough, watch it boot and see if the logo comes up before POST completes. Two, remove all HDDs and boot to BIOS. If you see the logo, it's before you get to a disk.
You can't change this by changing disks; it happens before a disk is used.
2) The boot then proceeds to the boot sector of a bootable drive, which loads the boot loader from that drive. My theory is that your Win10 installation saw the boot sector and loader on the HDD and did not install them on the SSD.
Note that this is after the POST process which runs in the BIOS.
3) The boot loader then loads the OS, in this case the Win10 on the SSD.