Since I don't use my mobile phone much like others. I want to mention me as in one word "this kind of person" who don't care much about mobile phones or attending calls. I know the word Nomophobia means fear of being without phone. But I couldn't find any opposite word for the word Nomophobia.
"Nomophobia" is essentially a joke word, made up in about 2008. It is not known by most speakers. It has not made it into most dictionaries (http://www.dictionary.com/misspelling?term=nomophobia) It is not considered a distinct medical condition by psychiatrists.
English doesn't have an authority that can decide on what is a word. In about 2008 someone made a joke, and a few other people have picked it up. However, you should not treat "nomophobia" as part of standard English.
The pattern "...phobia" is very productive. One can form lots of words by adding "phobia". The words created can be serious (claustrophobia - the fear of enclosed spaces) or jokey (Hippopotomonstrosesquippedaliophobia - the fear of long words) and new "phobias" are being invented all the time. Most of these words are used once and then forgotten.
There is also no standard term for "not being upset about not having a phone". Instead just explain. "I'm relaxed about not having my phone"