Renamed Functions
taxonomy_get_parents($tid) to taxonomy_term_load_parents($tid)
taxonomy_get_parents_all($tid) to taxonomy_term_load_parents_all($tid)
taxonomy_get_children($tid, $vid = 0) to taxonomy_term_load_children($tid, $vid = 0)
taxonomy_get_term_by_name($name, $vocabulary = NULL) to taxonomy_term_load_multiple_by_name($name, $vocabulary = NULL)

These changes were made prior to Backdrop's fork in the Drupal code base. An additional information may be found on drupal.org at #1377628: taxonomy_get_term_by_name() should be taxonomy_term_load_multiple_by_name().

Introduced in branch: 
1.0.x
Introduced in version: 
1.0.0
Impacts: 
Module developers
Related Github Issues: 
https://github.com/backdrop/backdrop-issues/issues/655