You could describe this as:
End-to-side anastomosis between left vena cava

This term is quite lengthy that I got it but would be suitable to follow the translation rule of always inserting the description in the brackets i.e. cavo-cavo LL (End-to-side anastomosis between left vena cava) so that the reader could understand what is what.

You can refer to the article provided as the reference by me.

Dans 5 cas sur 7 le diagnostic fut établi avant la transplantation grâce à l'écho doppler (complété une fois par une cavographie).
In 5 out of 7 cases, the diagnosis was established before transplantation by Doppler ultrasound (completed by cavography in one case).
https://dictionary.reverso.net/french-english/cavographie

Ce spécialiste pourrait vous faire passer une échographie pour essayer de voir les caillots dans le haut de la jambe ou une cavographie (une radiographie après injection d'une teinture) pour vérifier la présence de caillots dans le bas de la jambe.
Your specialist may use a diagnostic ultrasound to try to see clots in the upper leg, or a venography (x-ray with injected dye) to test for clots in the lower leg.
https://context.reverso.net/translation/french-english/cavog...

La cavography est un examen radiologique de la veine cave.
Cette veine, d'un diamètre important, transporte le sang des organes vers le cœur. L'examen nécessite l'injection d'un produit de contraste dans la veine fémorale, ou dans une veine périphérique. Cet examen est maintenant complètement abandonné; remplacé par l'échographie-doppler et les nouveaux scanners.
https://fr.wikipedia.org/wiki/Cavographie

Venography (also called phlebography or ascending phlebography) is a procedure in which an X-ray of the veins, a venogram, is taken after a special dye is injected into the bone marrow or veins. The dye has to be injected constantly via a catheter, making it an invasive procedure. Normally the catheter is inserted by the groin and moved to the appropriate site by navigating through the vascular system.
Contrast venography is the gold standard for judging diagnostic imaging methods for deep vein thrombosis; although, because of its cost, invasiveness, and other limitations this test is rarely performed.
https://en.wikipedia.org/wiki/Venography

In anatomy, a persistent left superior vena cava is the most common variation of the thoracic venous system.
In persistent left superior vena cava, the left brachiocephalic vein does not develop fully and the left upper limb and head and neck drain into the right atrium via the coronary sinus.
https://en.wikipedia.org/wiki/Persistent_left_superior_vena_...

La veine cave inférieure est une veine large située principalement dans l'abdomen, issue de la réunion des deux veines iliaques communes et qui s'ouvre dans l'atrium droit (anciennement oreillette droite) du cœur.
https://fr.wikipedia.org/wiki/Veine_cave_inférieure

Since most medical terms are derived from Latin, this should also apply to 'LL' (presumably double vena cavae, remainig from birth). I would leave it untranslated, as it can be assumed that the target audience understands the terms.