Question about the connection for a user

I have for my table 'Student' 5 fields id, name, firstname, email, phone.

My question: I would like the user to connect by putting his name what should I change?

    public function index(Request $request)
        {   
            $user = $request->user();
            $students= Student::query()
            ->when($user->hasRole('admin') !== true, function (Builder $query) use ($user) {
                $query->where('email', $user->email);
            })
            ->when($request->has('search'), function (Builder $query) use ($request) {
                $query->where('name', 'like', '%'.$request->input('search').'%');
            })
            ->paginate(5);
    
            
    
        return view('admin.students.index', compact('students'))
            ->with('display_search', $user->hasRole('admin'));
        }

Here:

    $query->where('email', $user->email);

I have to put this?

      $query->where('name', $user->name);

Thank you for your help.