The Barendregt convention is an assumption made when discussing the lambda calculus that declares each bound variable to be different from free variables (Barendregt, 1984, p. 26; Barendregt & Barendsen, 2000, p. 10).
This avoids having to deal with the name-capture problem.
In the 2004 errata for (Barendregt, 1984), Barendregt tries to course-correct the nomenclature adopted by academia:
This method was brought to my attention by Thomas Ottmann in 1972 and ever since I used it without refering [sic] to him (as it is so natural). After the appearence of this book the convention became baptized with my name. This is unjustified to Ottmann and for this reason I mention explicitly his name in these corrections.
Alas, sociolinguistic conventions are stronger than lambda calculus ones.