I try advice like this that recommends adding the following to your .profile:

function tabname {
    printf "\e]1;$1\a"
}

So you can type tabname brokenbox to name your tab. The problem is as soon as I also type ssh [email protected] and log in, it wipes the tab name. I want a tab name that's as persistent as the tab, not the level of session I happen to be in. Is this possible? I don't even know what layer that data lives in.