Saba Shahid... This is possible. Let me know what is current role of your user?

Definitely develop manual/custom plugin, because May some security issues we can avoid.

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There are might have the different type of ways to do that for different platforms. It needs to know which platform you are using to answer your question.

If you use WordPress there are plugins to implement the functionality.

By default, users can change their own profile information, including their email address, and excluding the username. To change the username, the user must have special permissions. To change the profile informations, go to example.com/user in your website, then click the "Edit" button.

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Do you want to allow user to update their profile, OR want to allow to change their username also?

Hi there,
To answer you question, it's simple if you're using wordpress.
There are plugins that will allow you to achieve it without much stress.