Looking at the screenshot provided, it is clear that renaming a selected tab requires clicking on it, while deleting an unselected tab necessitates a mouse hover. Unfortunately, these actions are not accessible via keyboard shortcuts. To address this issue, I propose assigning the F2 key to rename tabs - allowing users to simply press F2 when a tab is selected to rename it. Additionally, I suggest replacing the mouse hover for deleting tabs with a fixed delete button on each tab, making it accessible via keyboard commands.
Now, I am seeking solutions to both of these issues and can offer the CSS code needed to implement the delete button on the tab.
.js .delete-tab {
background: url(../images/common/remove.png) no-repeat 42%;
cursor: pointer;
display: block;
height: 8px;
position: absolute;
right: 2px;
text-indent: -9999em;
top: 2px;
width: 8px;
}