Nedarim 84B

וחכמים אומרים: קורא שם, ואין צריך להפריש. מאי לאו, למאן דאמר ספקו טובל, קסבר: אית ליה טובת הנאה, וכיון דאית ליה טובת הנאה ⁠— לא מהניא.

And the Rabbis say: He must designate poor man’s tithe by name, but he need not actually set it aside and give it to anyone, as a poor person cannot claim the tithe without bringing proof that he has a right to it. Rav Yosef now suggests: What, is it not that according to the one, i.e., the Rabbis, who says that the uncertainty as to whether or not poor man’s tithe had been separated by the am ha’aretz renders the produce forbidden as untithed produce [tevel], and therefore the owner of the produce must designate the poor man’s tithe by name, he holds that the owner of the produce has the benefit of discretion, meaning that he may give the poor man’s tithe to the poor person of his choice. And since he has the benefit of discretion, the option that a woman who vowed not to benefit from people should take poor man’s tithe is ineffective, as she would be receiving benefit from the owner of the tithe, since he could have given it to someone else.

ולמאן דאמר [אינו] קורא שם, קסבר: ספקו אינו טובל, וכל שספקו אינו טובל ⁠— לית ליה טובת הנאה, ושרי ליה לאיתהנויי.

Rav Yosef continues: And according to the one, i.e., R' Eliezer, who says that he need not designate poor man’s tithe by name, he holds that the uncertainty as to whether or not poor man’s tithe had been separated by the am ha’aretz does not render the produce forbidden as untithed produce. And whenever the case is that uncertainty does not render the produce forbidden as untithed produce, the owner does not have the benefit of discretion and does not choose to which poor person he will give it. And therefore one who vowed not to benefit from people is permitted to derive benefit from poor man’s tithe, as he is not receiving it from anyone.