可以尝试手动设置 Ethernet shield 的 DNS 服务器，以便正确的解析本地名称。

具体代码示例：

#include 
#include 

byte mac[] = { 0xDE, 0xAD, 0xBE, 0xEF, 0xFE, 0xED };
IPAddress server(192,168,1,100); // 服务器 IP 地址
char servername[] = "example.com"; // 服务器的本地名称
byte dnsServer[] = { 8, 8, 8, 8 }; // Google 的 DNS 服务器

EthernetClient client;
DNSClient dns;

void setup() {
    Ethernet.begin(mac);
    dns.begin(dnsServer);
    Serial.begin(9600);
}

void loop() {
    if (client.connect(server,80)) {
        Serial.println("Connected to server by IP");
        client.println("GET / HTTP/1.0");
        client.println();
        client.stop();
    } else {
        Serial.println("Connecting to server by name");
        dns.getHostByName(servername, server);
        if (client.connect(server,80)) {
            Serial.println("Connected to server by name");
            client.println("GET / HTTP/1.0");
            client.println();
            client.stop();
        } else {
            Serial.println("Connection failed");
            client.stop();
        }
    }
    delay(5000);
}