Why branding important

Branding is important because not only is it what makes a memorable impression on consumers but it allows your customers and clients to know what to expect from your company.
It is a way of distinguishing yourself from the competitors and clarifying what it is you offer that makes you the better choice

Bhar vs Bharosa brand effect comparison 

Bhar- 
no meaning
a misspelling word
no creativity while choosing the brand name
non memorable word

bharosa-
Hindi meaning trust
good world
consumer effective word and memorable word

Who suggested

At the lunch event of bhar os, IT Minister Ashwini Vaishnaw suggests that adding “a” to the name will make it Bharosa . (which means trust in Hindi).

Original name history

the name of the mobile os changes multiple times, before lunch.
1. First they call it -Ind Os
2. Secondly they call it-Bhar Os
3. Finally planning to change-Bharosa Os

Product About

BharOS is a mobile operating system designed by IIT Madras. 
It is an Indian government-funded project to develop a free and open-source operating system for use in government and public systems.

Company About

BharOS, developed by J and K Pvt. Ltd.
The company was incubated by the Indian Institute of Technology (IIT) Madras's  Pravartak Technologies Foundation.
The firm is Funded by the Indian Department of Science and Technology (DST) .
The company developed an Indigenous operating system for use with off-the-shelf commercial handsets.

Official confirmation

bhar os to Bharosa  OS change name - not officially announced.

Conclusion

if govt and company change its name from bhar to bharosa it should be a good step for India.