Welcome to the forums @MisterBNG!
I have not tried it myself, but I think the following code should work, or at very least the print statement may help indicate what is going on:
extends TabContainer
func _ready():
# Add tabs, etc.
var tab_count = get_tab_count()
print ("There are ", tab_count, " tabs")
# Get the first tab's current label
print ("First tab label: ", get_tab_title(0))
# Set the first tab's label
set_tab_title(0, "New Tab Title Here")
# make sure it's changed
print ("First tab label: ", get_tab_title(0))