The type species and only one currently recognized as valid by most researchers, is T. wellnhoferi.
The specific name honours German paleontologist Peter Wellnhofer.
Two larger species, originally named Tapejara imperator and Tapejara navigans, were later classified in the genus Tapejara.
However, several studies have shown that T. imperator and T. navigans are significantly different from T. wellnhoferi and therefore were reclassified into new genera.
The species T. imperator was given its own genus, Tupandactylus, by Kellner and Campos.
Unwin and Martill found that T. imperator and T. navigans belong in the same genus, and named them Ingridia imperator and I. navigans, respectively.
This genus name honoured Wellnhofer's late wife Ingrid.

Because Tupandactylus was named first, it retained priority over the name Ingridia.
To complicate matters, both the name Tupandactylus and Ingridia used the former Tapejara imperator as their type species.
The scientists who described Tupandactylus did not name a Tupandactylus navigans (but instead suggested it was synonymous to Tupandactylus imperator), and Tapejara navigans was not formally reclassified as a distinct species of Tupandactylus until 2011.

 
The cladogram below follows the 2014 analysis Andres and colleagues.
The type species and only one currently recognized as valid by most researchers, is T. wellnhoferi. The specific name honours German paleontologist Peter Wellnhofer. Two larger species, originally named Tapejara imperator and Tapejara navigans, were later classified in the genus Tapejara. However, several studies have shown that T. imperator and T. navigans are significantly different from T. wellnhoferi and therefore were reclassified into new genera. The species T. imperator was given its own genus, Tupandactylus, by Kellner and Campos. Unwin and Martill found that T. imperator and T. navigans belong in the same genus, and named them Ingridia imperator and I. navigans, respectively. This genus name honoured Wellnhofer's late wife Ingrid. 
Because Tupandactylus was named first, it retained priority over the name Ingridia. To complicate matters, both the name Tupandactylus and Ingridia used the former Tapejara imperator as their type species. The scientists who described Tupandactylus did not name a Tupandactylus navigans (but instead suggested it was synonymous to Tupandactylus imperator), and Tapejara navigans was not formally reclassified as a distinct species of Tupandactylus until 2011.
 
The cladogram below follows the 2014 analysis Andres and colleagues.
Tapejara (pterosaur)