I looked at alacritty but I really like using terminal tabs and the alacritty dev is really really against them and I found the dev's attitude to be more than a bit abrasive.
Not that Kovid (kitty's dev) does not come off the same way sometimes, but I tend to agree with Kovid a lot more.
Do check out wezterm. I didn't want to go into comparing developers but wez the main developer is a huge reason I prefer wezterm. They have tabs, panes, sessions, a mux implementation among many many other features.
I was looking for a way to get a user prompt within wez and came across this page which has an example for what you asked for "Example of interactively renaming the current tab".
I looked at alacritty but I really like using terminal tabs and the alacritty dev is really really against them and I found the dev's attitude to be more than a bit abrasive.
Not that Kovid (kitty's dev) does not come off the same way sometimes, but I tend to agree with Kovid a lot more.