Taxonomy term name alias in taxonomy term autocomplete
Two options to maybe investigate (neither are easy...):


You could create a custom module using hook_field_widget_form() to define a custom widget. There are several good tutorials on hook_field_widget_form out there, here's one I found quite useful, and the Form API Reference will help too. You might also want to look at Autocomplete Deluxe as a possible base.
You could create a Views table with autocomplete exposed filters, and some custom javascipt that binds a click event to each row controlling the form element, and you could use the 'Node edit' override in Ctools page manager to customise the form page and add it in. If you want one autocomplete box to filter both 'Name' and 'Synonyms', you might need some custom javascript again: maybe hide one input box and control its input with a jquery keyup event on the other box, and set the contextual filters to 'Or' in Views


Of these I'd recommend the first way - much cleaner and probably less work!