Do you have health problems like diabetes? Then it is good to keep an eye on them.
As long as you eat an overall balanced diet and are generally healthy, there are no special blood tests requirements for intermittent fasting.

If you want to you can always ask your GP to check urea+electrolytes, liver function, blood glucose and cholesterol. Your GP is likely to test that occasionally, like once a year, as a general check up on request but unless you are paying privately he is unlikely to do it every month. Most of these tests are unlikely to change much due to fasting.