For three years, Jesus poured out His love on His disciples, attempting to form them into bold witnesses. Jesus repeatedly taught His disciples to forsake all to follow Him (e.g. Mt 16:24ff; Lk 9:23ff). In the moment Jesus most needed loyalty from His disciples, they forsook all to flee Him (Mk 14:50).
"All deserted Him and fled. There was a young man following Him who was covered by nothing but a linen cloth. As they seized him he left the cloth behind and ran off naked" (Mk 14:50-52). Jesus had said: "None of you can be My disciple if he does not renounce all his possessions" (Lk 14:33). This disciple certainly renounced his possessions — and even his clothes — but he renounced them to disassociate himself from Jesus.
Peter renounced his identity as a Galilean, a disciple, and even the fact that he knew Jesus (Mk 14:67-71). He began to curse, and to swear, "I do not even know the Man you are talking about!" (Mk 14:71) Peter indeed chose to lose his very identity, his very self — but only to be seen as not knowing Jesus.
Lose everything — but for the right reason. We won't get off this earth without losing it all (see Jb 1:21): our life, money, possessions, reputation, loved ones, etc. The only thing we take with us from this life is our bond with the Lord. Jesus "died for all so that those who live might live no longer for themselves, but for Him" (2 Cor 5:15). Choose to lose — anything that separates you from being known as a disciple of Jesus.