Is blood transfusion really needed right away for a 86 years old patient with creatinine level of 3.6 and hemoglobin of 61?

Possibly.: Difficult question to answer. Depends upon a lot of factors that aren't laid out here. The patient sounds to be seriously in trouble although there are lots of ways to get to those numbers and not all of them require immediate transfusion.

6.1 Hb: Probably, if patient is unstable or hypotensive or bleeding. Rate of decline in hb should also be taken into account. Iron infusion & erythropoietin may be indicated. Transfusion should be given slowly for a renal failure patient.

Yes most likely: It depends upon your goals of care. A hemoglobin of 6.1 is very low. Having enough red blood cells would probably help her (kidneys) creatinine to improve. Is she weak? Fatigued? It would probably help her to feel much, much better overall to be running on a full tank.

Blood transfusion?: If the patient is hypotensive and has a rapid heart rate, a blood transfusion is mandatory. A hemoglobin (h) of 6.1 is about 30% that of a normal h of. Unless the patient is in hospice care, the patient, or the patient's family, should be offered the option of a blood transfusion to elevate the h to a level > than 10 gm/dl.