Add custom properties to Serilog

This is as simple as:

Log.ForContext("BirthDate", person.BirthDate)
   .Information("New user: {FirstName:l} {LastName:l}",
                           person.FirstName, person.LastName);

You can actually do this in a few different ways. In your case, the first way is probably the best:

Log.ForContext("BirthDate", person.BirthDate)
    .Information("New user: {FirstName:l} {LastName:l}",
        person.FirstName, person.LastName);

But you can also use the LogContext in other scenarios:

Log.Logger = new LoggerConfiguration()
    // Enrich all log entries with properties from LogContext
    .Enrich.FromLogContext();

using (LogContext.PushProperty("BirthDate", person.BirthDate))
{
    Log.Information("New user: {FirstName:l} {LastName:l}",
        person.FirstName, person.LastName);
}

Or, in the case where you want to log a "constant" property, you can add it like this:

Log.Logger = new LoggerConfiguration()
    // Enrich all log entries with property
    .Enrich.WithProperty("Application", "My Application");

See Context and correlation – structured logging concepts in .NET (5) for more information.