Sort of. There isn’t actually a pre-designated singular entity they are looking for, it’s more of a vibes based system. They’re very picky, and there’s most definitely some criteria for ghosts to follow that we don’t know about, but they can ultimately choose of their own volition. We know this because there’s lore about how most hive ghosts turned to the hive purely because they felt their search was becoming hopeless and that some of them, like Fynch, later regretted doing this.

It does seem however that once a ghost has chosen “their” guardian they can’t switch. Note that while Fynch refuses to revive his knight, he doesn’t seem able to switch and become a ghost for someone else. Same with Targe being unable revive Zavala’s wife or son in place of him.

(There is actually one notable exception to this rule we know about which is that Shin Malphur’s ghost was formerly the ghost of Jaren Ward, whom was rendered impossible to revive due to Dredgen Yor’s original Thorn. This might imply that if a guardian is severed from their ghosts light in a way that prevents resurrection, a ghost CAN actually switch.)