Inject DbContext when database name is only know when the controller action is called

You can/should use an abstract factory to create the DbContext

public interface IDbContextFactory
{
    ApplicationContext Create();
}

public class DbContextFactory() : IDbContextFactory, IDisposable
{
    private ApplicationContext context;
    private bool disposing;

    public DbContextFactory(/* other dependencies here */)
    {
    }

    public ApplicationContext Create(string tenantId) 
    {
        if(this.context==null) 
        {
            // and the connection string and replace the database name in it
            // with the tenantId or whatever means you have to determine
            // which database to access
            string connectionString = ...;

            var dbContextBuilder = new DbContextOptionsBuilder();
            dbContextBuilder.UseSqlServer(connectionString);

            this.context = new ApplicationContext(dbContextBuilder);
        }

        return this.context;
    }

    public void Dispose(){
        Dispose(true);
        GC.SuppressFinalize(this);
    }

    protected virtual void Dispose(bool disposing){
        if (disposing){
            disposing?.Dispose();
        }
    }
}

Register it

services.AddScoped<IDbContextFactory, DbContextFactory>();

and use it in your controllers as following

public class MyController : Controller
{
    private readonly IDbContextFactory contextFactory;

    public MyController(IMyContextFactory contextFactory)
    {
        this.contextFactory = contextFactory;
    }

    public Task<IActionResult> GetSomeData(string tenantId)
    {
        var context = contextFactory.Create(tenantId);

        return Ok(await context.Data.Where(...).ToListAsync());
    }
}