Until about two months ago, my mom had always had a cat named Gustav as long as I’ve been around (32 years). Gustav I (1963-1981) and Gustav II (1981-2002) were both great cats and I never found it to be odd that they were named the same. They were both called Gustav; but in terms of conversation and name attribution, they were identified with their appropriate members of the royal family.
In terms of the re-naming of humans, it does seem a little spooky. My paternal grandmother’s parents had their first son George round about 1890 or so. George died as a toddler of Reubella (I think). The next boy born after George’s death was also named George. This son was killed by a sniper in WWI. It has been a topic of family discussion among the more superstitious relatives that the son who died in the war might have been cursed (I hate to use that word, but I can’t find the term that sounds right).
With pets, I never gave renaming too much thought. I know that some friends had said that it was odd, but it never really sent-up any flags for me. The renaming of humans is another story entirely. If the family feels comfortable with the renaming of a child after the name of a deceased sibling; that’s great. It just strikes me as sort of unsettling.