Tosafos discusses the issur of chodosh in light of the mishna where R' Elazar considers it to be something applicable in chutz la'aretz. Tosafos writes that most of the grains planted were planted prior to 16 Nissan so there would not be a problem of chodosh. It is only if someone knows specifically that this grain was planted after, that it is assur. The problem is that nowadays there isn't necessarily a rov that the grain is yoshon, so the poskim try to justify why we are not makpid about chodosh:
1. Rama - Even if there is no rov that the grain is yoshon, there is at least a s'fek s'feika, maybe the tevuah is from last year, and even if it is from this year, maybe it was planted after 16 Nissan. When there isn't a s'fek s'feika such as when it is known that the planting is done after pesach, the Rama says that one should be machmir (but not tell others since mu'tav she'yihyu shogigin). The difficulty with this approach is twofold - A. Chodosh is a davar sheyesh lo matirin where some are machmir even for a s'fek s'feika (shach). B. R' Akiva Eiger (and teshuvos mutzal me'eish) ask that based on the concept of שם אונס חד הוא, a sfeik sfeika has to have 2 independent rationales to be permitted, not just 2 way that it can be last years grain.
2. Bach - Argues on Tosafos and proves from the Yerushalmi that chodosh doesn't apply to grain that was from the field of a gentile. The taz and shach strongly disagree. The Gr"a also says that the achronim already "hit him over the head".
3. Taz - Considers the fact that there is a machlokes ta'naim whether it applies outside of Israel, and says that in a pressing situation we can pasken like the tana kama of our mishna that it only applies in Eretz Yisroel. Magen Avrohom also takes this approach. The Shach in nekudas hakesef strongly rejects the Taz.
The Gr"a concludes that the only legitimate heter is the Rama that it is a s'fek s'feika. Regarding the question of "shem o'nes chad hu", it must be that since there are 2 distinct ways that it can be last years produce, one that it actually is last years produce, and another that even if it is this years maybe it took root before pesach, it qualifies as a s'fek s'feika.
Regarding the second question on the Rama that it is a davar she'yesh lo matirin, R' Moshe (Igros Moshe Y.D. 4:46:4) explains that the shach answers this in two ways: 1. The only time we don't allow sfeik sfeika to be matir a davar sheyesh lo matirin, is when it is a mixture that definitely contains the issur. But here where the grain in that each individual is deciding on eating may not contain chodosh at all, we can use sfek sfeika to be matir. 2. In a situation where it is a tzorech we can rely on the opinions who allow sfek sfeika even by davar sheyesh lo matirin. R' Moshe holds that nowadays the tzorech is much less than it was, so the second approach is no longer valid, but the first approach is still valid.