(I) Allah didn't name this religion (Abraham named us "Muslims" only). The name of this religion is "Islam", it means "obedience", and Quran uses that name for its literal meaning, not for naming the religion.

(II) In order for someone to be salvaged from hell, he must be a Mumin and must have done good deeds. The word "mumin" comes from the root "امن", and one of its etymological meaning is "to be safe". Being a Mumin is nothing but being in the safe line called "suratal mustakim". There is a lot of ayats in Quran saying that those who are Mumin and who did good deeds will be salvaged for sure, but there is no ayat in Quran saying that a Muslim will be salvaged for sure.

(III) It is possible that someone heard bad things about Islam on TV, did hear its rightful explanation from anyone, hated it by name only. But somehow lived as a Mumin. Stayed away from shirk, did good deeds, did salat according to his own way and understanding and Allah accepted that, etc. Then he is a Mumin.

If you combine (I), (II) and (III) then you understand the ayat 2:62. Quran states that some of ahlul kitab are Mumin, even though they are defining themselves as Christian, Jew, etc. This is a fact. Defining yourself as a Muslim does not make you a Muslim. Defining yourself as an Atheist does not make you a pagan; there are some pagans who oppose the wrong definition of Allah, so they are opposing this wrong definition by saying "There is no Allah!" by their mouth, but they live a better life than an ordinary Muslim does. Quran is mentioning this fact in that ayat.

An extra information and thinking exercise:
Animals and plants are not Muslim (they are living according to their own desires), but they are Mumin (Satan did not deceive them and lured them out of Cannat as he did to human race by Adam). So, being a Mumin is theoretically possible without being a Muslim.

(I) Allah didn't name this religion (Abraham named us "Muslims" only). The name of this religion is "Islam", it means "obedience", and Quran uses that name for its literal meaning, not for naming the religion.

(II) In order for someone to be salvaged from hell, he must be a Mumin and must have done good deeds. The word "mumin" comes from the root "امن", and one of its etymological meaning is "to be safe". Being a Mumin is nothing but being in the safe line called "suratal mustakim". There is a lot of ayats in Quran saying that those who are Mumin and who did good deeds will be salvaged for sure, but there is no ayat in Quran saying that a Muslim will be salvaged for sure.

(III) It is possible that someone heard bad things about Islam on TV, did hear its rightful explanation from anyone, hated it by name only. But somehow lived as a Mumin. Stayed away from shirk, did good deeds, did salat according to his own way and understanding and Allah accepted that, etc. Then he is a Mumin.

If you combine (I), (II) and (III) then you understand the ayat 2:62. Quran states that some of ahlul kitab are Mumin, even though they are defining themselves as Christian, Jew, etc. This is a fact. Defining yourself as a Muslim does not make you a Muslim. Defining yourself as an Atheist does not make you a pagan; there are some pagans who oppose the wrong definition of Allah, so they are opposing this wrong definition by saying "There is no Allah!" by their mouth, but they live a better life than an ordinary Muslim does. Quran is mentioning this fact in that ayat.

An extra information and thinking exercise:
Animals and plants are not Muslim (they are living according to their own desires), but they are Mumin (Satan did not deceive them and lured them out of Cannat as he did to human race by Adam). So, being a Mumin is theoretically possible without being a Muslim.