Change the label of the GtkButton

ptomato is right you are using ==

where you should be using =

.
Your code should look like this:

char *ButtonStance = "Connect";
GtkWidget *EntryButton = gtk_button_new_with_label(ButtonStance);

gtk_box_pack_start(GTK_BOX(ButtonVbox), EntryButton, TRUE, TRUE, 0);

gtk_box_pack_start(GTK_BOX(TopVbox), ButtonVbox, TRUE, TRUE, 0);

gtk_widget_show_all(TopVbox);

ButtonStance = "Disconnect";

gtk_button_set_label(GTK_BUTTON(EntryButton), ButtonStance);

gtk_main();