Many may have such thoughts, thankfully most realise that life has its downs and its ups and if one sticks in there things eventually get better; and then they are glad they didn't go through with anything rash.
Strange to consider that a safety net for surely nothing could be less safe. One needs to avoid just looking for any way out of one's present mental state, and look instead to ways to cope in the meanwhile.
Try not to take the burden of the world as your own personal thing to shoulder. It isn't reasonable. You can not expect others to act as you do, some will do better, others worse, and for sure you'd not want everyone to act better than yourself, so one has to accept the range of human beings we have.
As for identity, you are who you are, why do you need to categorise yourself ? And why should you feel saddened if you can't ? Try to accept and prioritise the things that really matter.