diff --git a/packages/appium/lib/appium.js b/packages/appium/lib/appium.js
index 8c6e775ea..82f0da473 100644
--- a/packages/appium/lib/appium.js
+++ b/packages/appium/lib/appium.js
@@ -66,7 +66,7 @@ class AppiumDriver extends BaseDriver {
    */
   get log () {
     if (!this._log) {
-      const instanceName = `${this.constructor.name}@${node.getObjectId(this).substring(0, 8)}`;
+      const instanceName = `${this.constructor.name}@${node.getObjectId(this).substring(0, 4)}`;
       this._log = logger.getLogger(instanceName);
     }
     return this._log;
diff --git a/packages/base-driver/lib/basedriver/driver.js b/packages/base-driver/lib/basedriver/driver.js
index 9d9e30119..8b6f60a50 100644
--- a/packages/base-driver/lib/basedriver/driver.js
+++ b/packages/base-driver/lib/basedriver/driver.js
@@ -108,10 +108,21 @@ class BaseDriver extends Protocol {
 
   get log () {
     if (!this._log) {
-      const instanceName = `${this.constructor.name}@${node.getObjectId(this).substring(0, 8)}`;
-      this._log = logger.getLogger(() =>
-        this.sessionId ? `${instanceName} (${this.sessionId.substring(0, 8)})` : instanceName
-      );
+      const instanceName = `${this.constructor.name}@${node.getObjectId(this).substring(0, 4)}`;
+      // We don't want the self reference to be captured inside the below closure
+      // to avoid possible memory leaks,
+      // but NodeJS started supporting WeakRef only since v. 14.6
+      const self = global.WeakRef ? new global.WeakRef(this) : this;
+      this._log = logger.getLogger(() => {
+        let sessionId = self?.sessionId;
+        if (!sessionId && _.isFunction(self.deref)) {
+          const ref = self.deref();
+          if (ref?.sessionId) {
+            sessionId = ref.sessionId;
+          }
+        }
+        return sessionId ? `${instanceName} (${sessionId.substring(0, 8)})` : instanceName;
+      });
     }
 
     return this._log;