The book Quran describes people according to their thinking pattern that forms the base of our behavior. It does not discuss our appearance. It is a book of universal truth and does not specifically target any specific community. Muslim, Momin, Mushrik, Kafir, Munafiq, Fasiq, Yahood, Nasara are not communities or sects but they are human mindset that forms our behaviour.
It doesn't matter if you have a beard, if you wear a religious dress, or have an Arabic name or Sanskrit name, or any of the dozens of superficial expressions of faith that religious people carry.
"Muslims" generally place a higher value on superficial appearance because they believe that's what prophet Muhammad was like and copying him is an act of righteousness. Such thinking is against Islamic way of thinking. Imitation has no place in Islam. The main emphasis of the book Quran is to think, ponder, meditate, reason, verify, check and don't follow anything blindly.
Note, the book Quran talks only about human mindset and behaviors and the consequences of not having a sound and balance mindset, copying or imitating Arabic culture is not Islam.
Islam or Peacefulness comes by accepting each other, understanding each other, respecting each other, working with each other, speaking the language of the locals, participating in each other's happiness and grief. Understanding our limits is Islam, going out of limit is not Islam. Peaceful living is Islam. Recognizing our Satan and our true God is Islam. Blind worship is not Islam. Establishing the Kingdom of Your God is not Islam. Accepting and respecting every culture is Islam
"The servants of Rehman are they who walk in the earth / ardh with humility, and when the ignorant address them, they say: Peace." - Quran 25:63
"And they who do not bear witness to lies, and when they pass by vanity, they pass by it with dignity.
And those who, when reminded of the ayaat / communications of their Rabb, do not act as if they were deaf and blind" - They think, reflect and are mindful, thoughtful, cautious...
So if you aren't behaving as the Quran describes; your beard, your thawb, your hijab, your eating habits or whatever else you have incorporated into your identity will not help you. The best dress is modesty or taqwa, not tailor-made religious cloths. The words of the Quran address your thoughts that form your behavior, your inner mechanism that controls your senses and if you don’t understand those ayaats / signs then you have a major problem.
On the other hand, if your behavior is peaceful and you love and respect everyone and for you work is worship then you don't need anything else, you are already there, you just have to keep it up. You don't have to grow a beard, change your name, and wear clothes foreign to your culture or anything like that. If you still want to perform a ritual that’s okay but if your behavior is on point that's all that matters. Creating a different personality away from the culture we live is inviting doubt, suspicion and isolation from the mainstream locals and that is not good for you.
Behavior / Attitude is the goal of life, that is what the book Quran says. All of us are supposed to incorporate that thought process that molds the behavior into our identities or die trying, which is the goal of this life. It's hard but anyone can do it with enough of dedication and discipline.
Don't work on making your fake appearance your identity. Muslim identity is not putting on makeup; it is your mindset, your behaviour, your humble attitude, your care and love for everyone.
Work on what the Quran says is important - the thought process, the behavior. Mold your identity to correspond to behavior beneficial to the people you live with, then only you are a true servant of God no matter your name or your appearance. If you fail to do that then nothing will help you.