Another good reason to remove hdd is, apart from win 10 seeing itself on hdd and probably wanting to install there, if you leave the hdd in and installed onto ssd, the installer is likely to use the boot partition on the hdd for the ssd, meaning that if you ever removed hdd, the ssd wouldn't boot.
if you put hdd back in, make sure the bios doesn't add it to the boot order or pc might accidentally boot from it at a later time.
ideally, you best copy anything off hdd you want to keep and formatting it later. Here is how:
boot from installer
on screen after languages, choose repair this pc, not install.
choose troubleshoot
choose advanced
choose command prompt
type diskpart and press enter
type list disk and press enter
this shows all drives available, DVD/USB and hdd, make note of hdd number
type Select disk X - where X is the number of the hdd you want to wipe, change X to that number and press enter (make sure not to choose ssd by mistake)
Once the drive you want to wipe is chosen, type Clean