In Bereshis 17:5 is when Avraham's name is changed.
We see however that Rashi until then referred to Avraham as "Avram". For example Rashi in Bereshis 11:32
"...לאחר שיצא אברם"
This is certainly reasonable that when one is learning the pasukim in a time when Avraham was still called Avram that we would refer to him by the name that he has called at that point in the Torah.
However after Avraham's name was changed in the Torah we see Rashi changes the way he referrs to him even in a time when he was still called Avram. See Rashi in Bereshis 19:20,
"...ומשם עד שנולד אברהם שבעים"
Since the Torah has already changed his name Rashi will refer to him in such a way even when mentioning a time when he was not called yet "Avraham".
Rashi on the Gemorah in Avodah Zara (Daf 19a d'h Avraham Avinu) also refers to Avraham by this name even referring to him in a time when he was still called Avram.
אברהם אבינו. בימי דור הפלגה היה בסוף ימי פלג נפלגה הארץ כדתניא בסדר עולם א"ר יוסי נביא גדול היה עבר שקרא לבנו פלג וא"ת בתחילת ימיו כו' ופלג ראה את אברהם כמה שנים דהא לקצ"א דפלג נולד אברהם וחיה פלג אחר כך כמה שנים
To answer the question I think we see from here that one must call "Avraham" by that name even when referring to him in a time when he was still called Avram (unless of course one is learning the pasukim when he was still called Avram.)