What is the way in ASP.NET Core 3.0 to get current authenticated User username?

You can use IHttpContextAccessor

private readonly IHttpContextAccessor _httpContextAccessor;

public UserService(
    IHttpContextAccessor httpContextAccessor)
{
  _httpContextAccessor = httpContextAccessor;       
}

And to get user name you can use

_httpContextAccessor?.HttpContext?.User?.Identity?.Name;

Or

 _httpContextAccessor.HttpContext.User.FindFirstValue(ClaimTypes.NameIdentifier);

Then register in your Startup.cs

public void ConfigureServices(IServiceCollection services)
{
    services.TryAddSingleton<IHttpContextAccessor, HttpContextAccessor>();
}

For this issue, it is caused by that the IdentityServer4 did not add the JwtClaimTypes.Name to the access_token. If you check the access_token from web brower, you will find it miss "name": "Tom", node.

For a workaround, you could implement your own ITokenService like

public class CustomTokenService : DefaultTokenService
{
    public CustomTokenService(IClaimsService claimsProvider
        , IReferenceTokenStore referenceTokenStore
        , ITokenCreationService creationService
        , IHttpContextAccessor contextAccessor
        , ISystemClock clock
        , IKeyMaterialService keyMaterialService
        , ILogger<DefaultTokenService> logger) 
        : base(claimsProvider, referenceTokenStore, creationService, contextAccessor, clock, keyMaterialService, logger)
    {
    }

    public override async Task<Token> CreateAccessTokenAsync(TokenCreationRequest request)
    {

        Logger.LogTrace("Creating access token");
        request.Validate();

        var claims = new List<Claim>();
        claims.AddRange(await ClaimsProvider.GetAccessTokenClaimsAsync(
            request.Subject,
            request.Resources,
            request.ValidatedRequest));

        if (request.ValidatedRequest.Client.IncludeJwtId)
        {
            claims.Add(new Claim(JwtClaimTypes.JwtId, CryptoRandom.CreateUniqueId(16)));
        }
        claims.Add(new Claim(JwtClaimTypes.Name, request.Subject.GetDisplayName()));
        var issuer = Context.HttpContext.GetIdentityServerIssuerUri();
        var token = new Token(OidcConstants.TokenTypes.AccessToken)
        {
            CreationTime = Clock.UtcNow.UtcDateTime,
            Issuer = issuer,
            Lifetime = request.ValidatedRequest.AccessTokenLifetime,
            Claims = claims.Distinct(new ClaimComparer()).ToList(),
            ClientId = request.ValidatedRequest.Client.ClientId,
            AccessTokenType = request.ValidatedRequest.AccessTokenType
        };

        foreach (var api in request.Resources.ApiResources)
        {
            if (!string.IsNullOrWhiteSpace(api.Name))
            {
                token.Audiences.Add(api.Name);
            }
        }

        return token;
    }
}

And then register CustomTokenService before Identity Configuration

    public void ConfigureServices(IServiceCollection services)
    {
        services.TryAddTransient<ITokenService, CustomTokenService>();

        services.AddDbContext<ApplicationDbContext>(options =>
            options.UseSqlServer(
                Configuration.GetConnectionString("DefaultConnection")));

        services.AddDefaultIdentity<ApplicationUser>()
            .AddEntityFrameworkStores<ApplicationDbContext>();

        services.AddIdentityServer()
            .AddApiAuthorization<ApplicationUser, ApplicationDbContext>();

        services.AddAuthentication()
            .AddIdentityServerJwt();

    }

For a simple way, you could try to override DefaultClaimsService.GetStandardSubjectClaims like

public class CustomClaimsService : DefaultClaimsService
{
    public CustomClaimsService(IProfileService profile
        , ILogger<DefaultClaimsService> logger) : base(profile, logger)
    {
    }
    protected override IEnumerable<Claim> GetStandardSubjectClaims(ClaimsPrincipal subject)
    {
        var claims = base.GetStandardSubjectClaims(subject);
        var newClaims = new List<Claim>(claims)
        {
            new Claim(JwtClaimTypes.Name, subject.Identity.Name)
        };
        return newClaims;
    }
}

And register like

    public void ConfigureServices(IServiceCollection services)
    {
        services.TryAddTransient<IClaimsService, CustomClaimsService>();

        //services.TryAddTransient<ITokenService, CustomTokenService>();

        services.AddDbContext<ApplicationDbContext>(options =>
            options.UseSqlServer(
                Configuration.GetConnectionString("DefaultConnection")));

        services.AddDefaultIdentity<ApplicationUser>()
            .AddEntityFrameworkStores<ApplicationDbContext>();

        services.AddIdentityServer()
            .AddApiAuthorization<ApplicationUser, ApplicationDbContext>();

        services.AddAuthentication()
            .AddIdentityServerJwt();

    }