Why doesn't the terminal window title change when logging into OpenBSD from Linux Mint?

From a Linux Mint terminal window, when I ssh into OpenBSD, the terminal window title remains the same as just the terminal username@localhostname:~, whereas logging into Ubuntu the terminal window title will change to username@remotehostname:~. I have certainly found *many* solutions to fix this problem, but the solutions seem to be of many different sorts and rarely seem to be addressing the specific shells I am using. So rather than good ol' "guess-and-check" to figure out which solution is for me, I would prefer to understand why I am having this problem in the first place so I can move to the next step of discovering a solution. Why doesn't the terminal window title change when using ssh to log into OpenBSD with Linux Mint?