If we add up all the income while finding GDP of a country, is income counted multiple times? Suppose 9 others and I are government employees. We get salary which will be counted while calculating GDP. Let's assume that we 10 are the only customers of a shop (for simplicity). The shopkeeper's income is derived from the 10 of us. Now if we calculate the shopkeeper's income while calculating GDP, then the the income will be counted twice since it was counted as our income at first place. So how are situations like this handled?
There is no contradiction here. All these incomes are part of the GDP. In theory all incomes show the value of something. In your example this would be the value of the work done. Since all 10 government employees and the shopkeeper are working they all create value, the size of which is measured by adding up their salaries.

Here you can find an explanation of what GDP exactly is.