mission control – Names of Spaces – “Safari” vs [Website name]

I use Spaces a ton. I recently used my wife’s MBA, and was surprised to see that when I put safari into full screen and hit f3 to show all windows and spaces, the space with safari was named [name of website], where as on my computer (Mac Studio, Ventura 13.2.1) it just says “Safari.” I cannot figure out what the difference is. I’d love for my computer to say the name of the active website.
Any ideas on how if there is a setting something somewhere that would effect this?