AsyncLocal

Person.cs

public class Person
{
    public string Name { get; set; }
}

Program.cs

using System;
using System.Threading;
using System.Threading.Tasks;

public class Program
{
    private static AsyncLocal<Person> LocalPerson { get; } = new AsyncLocal<Person>();
    private static ThreadLocal<Person> ThreadPerson { get; } = new ThreadLocal<Person>();

    public static async Task Main(string[] args)
    {
        LocalPerson.Value = new Person { Name = "John" };
        ThreadPerson.Value = new Person { Name = "Jane" };
        await BeBobAndSara();
        await PrintPerson();
    }

    private static async Task BeBobAndSara()
    {
        await Task.Delay(0);
        LocalPerson.Value = new Person { Name = "Bob" };
        ThreadPerson.Value = new Person { Name = "Sara" };
    }

    private static async Task PrintPerson()
    {
        await Task.Delay(0);
        Console.WriteLine(LocalPerson.Value?.Name);
        Console.WriteLine(ThreadPerson.Value?.Name);
    }
}