Investigative work might uncover how likely it is that Reuven is a levi. However, we cannot to do that for you, at least not without additional information. A last name may give a reasonable indication, although rarely is it conclusive. Based on the information you provided, it does not appear likely that he is a levi. The passing statement of a non-observant Jew carries little weight, given that he might not even have known what a levi is and that his statement was further firmly contradicted by someone who is likely to know as well as he. Thus, for example, Reuven cannot assume that his lineage would exempt his firstborn son from a pidyon haben, as it would in the case of a levi.[1] The question is whether it is acceptable to allow Reuven to continue getting the second aliya, which is reserved for levi’im, in order to make him feel more settled by not dismissing his previous assumption outright, even though it is probably not objectively warranted.
The gemara[2] discusses the case of one who was assumed to be a levi due to the fact that his community regularly gave him the second aliya. The Ran[3] derives from this gemara that someone who claims without proof that he is a levi should not receive the second aliya, as this could later be used as proof regarding other matters (e.g., receiving ma’aser rishon). The same is true in the case of a kohen and the first aliya. Nevertheless, the Ran says, the prevalent practice is to believe people without proof. He suggests that since terumot and ma’asrot[4] are now rabbinic and uncommon, we are not so strict in determining who is deserving of the special aliyot. However, the Ran accepts the Rambam’s[5] opinion (stated regarding a possible kohen) that we do not give the special aliyot without proof.
Must we assume that the stakes are high enough for a levi to equate the rule for him to that of a kohen and withhold the second aliya due to inadequate proof of eligibility?[6] The Yam Shel Shlomo[7] rejects the lenient minhag of trusting kohanim regarding aliyot and explains that even though there is no teruma at present, the laws regarding who can perform nesi’at kapayim[8] are also mandated by the Torah. Also, he says, we must consider the hopefully imminent rebuilding of the Beit HaMikdash. Whereas the first issue does not apply to levi’im, the Beit HaMikdash is relevant. After all, a non-levi who mistakenly does a levi’s work violates a serious prohibition.[9] The Yam Shel Shlomo’s logic would therefore limit us from giving the second aliya to one of questionable levi status.
The Chazon Ish[10] says that nowadays, no one really deserves to be called up as a levi. Such a long period has passed since authorities checked lineage before aliyot that no one has adequate proof. Our doubts on the matter explain why we do not give them ma’aser. According to the Chazon Ish, one could say that it does not matter much that your friend also takes the title of levi. However, it seems that a case of a pidyon haben would raise an issue of doubt. In any case, here, where even the subject does not really claim that he is a levi, but just that he might be one, he should not get the second aliya.
The Shulchan Aruch records the takana that the kohen’s aliya should be followed specifically by that of a levi, lest we lead others to think that the kohen is not valid and thus violate his honor.[11] If we were to treat Reuven as a levi and he is not actually one, would we violate this takana? Logic dictates that if everyone presumes Reuven to be a levi, this would not be a concern. To the contrary, one could claim that if we change his presumed status and begin to give him the third aliya, it might give the impression that the previous levi was not authentic.[12] Therefore, we suggest that until people get accustomed to the fact that Reuven is now presumed to be a yisrael, he should not get the aliya directly after levi (i.e., he should receive aliyot only on Shabbat and Yom Tov from revi’i on).