concealing one's imaan

New Muslim publicly professing his Imaan

Q:

1. Is it necessary for a new Muslim to publicly profess their Imaan?

2. Under what circumstances will it be permissible to hide one's own Imaan?

3. If a person dies hiding their Imaan, how will the Muslim public ascertain that this person was a Muslim? For example, if a person continued to live with their non-Muslim partner; did not dress as a Muslim; did not make a request for a Muslim funeral and did not change their name, would this be sufficient evidence to not classify them as Muslim?