Iron Deficiency Anemia: This is the most likely diagnosis given the low iron level (3 umol/L), low iron saturation (0.06), and elevated TIBC (51 umol/L), which are all indicative of iron deficiency. The ferritin level of 71 ug/L, although within the normal range for some labs, can be considered low in the context of puberty and menstrual losses, supporting this diagnosis. The hemoglobin of 122 g/L is slightly below the normal range for a female of this age, further supporting iron deficiency anemia.

Anemia of Chronic Disease: Although less likely given the low iron and high TIBC, anemia of chronic disease could be considered if there's an underlying chronic condition. However, the iron saturation and TIBC levels are more suggestive of iron deficiency than anemia of chronic disease.
Thalassemia Trait: This could be a consideration given the slightly low hemoglobin, but the iron studies do not support a diagnosis related to thalassemia, which typically would not affect iron, TIBC, or ferritin levels in this manner.

Celiac Disease: This is an important diagnosis not to miss, as it can lead to iron deficiency anemia due to malabsorption. Although the iron studies suggest iron deficiency, celiac disease could be an underlying cause and requires serological testing for diagnosis.
Chronic Blood Loss: Not just from menstruation, but also from gastrointestinal sources (e.g., ulcers, inflammatory bowel disease) or other sites. Chronic blood loss can lead to iron deficiency anemia and should be investigated, especially if menstrual losses are not considered sufficient to cause the degree of iron deficiency observed.

Transferrinemia or Atransferrinemia: These are rare genetic disorders affecting transferrin, the protein that binds iron in the blood. They could potentially cause abnormal iron studies, but are exceedingly rare and would not typically be considered without other supporting evidence or family history.
Hemoglobinopathies (other than Thalassemia): Certain hemoglobinopathies can affect hemoglobin levels and potentially interact with iron metabolism, but these would be rare and typically identified through hemoglobin electrophoresis or other specific tests.