How to know if a bot claimed to be Googlebot a real Googlebot? Verify Googlebot

The answer is running Google DNS reverse lookup.

Let's see some straight forward examples:

Example 1:

> host 66.249.66.1
1.66.249.66.in-addr.arpa domain name pointer crawl-66-249-66-1.googlebot.com.

> host crawl-66-249-66-1.googlebot.com
crawl-66-249-66-1.googlebot.com has address 66.249.66.1

Example 2:

> host 66.249.90.77
77.90.249.66.in-addr.arpa domain name pointer rate-limited-proxy-66-249-90-77.google.com.

> host rate-limited-proxy-66-249-90-77.google.com
rate-limited-proxy-66-249-90-77.google.com has address 66.249.90.77

Reference: //support.google.com/webmasters/answer/80553?hl=en