As far as I know μ is used to define true population mean.
Not quite, and here's the rub. μ represents whatever the true mean is. It's defined by the problem for which this little bit of statistical inference is the analysis, not by the data itself (that would make it an estimate, not a hypothesis)
So in formula above I need true population mean μ to calculate t-score.
You need a hypothesis about what it is, that is: a possible value for it. You dont need to know what that value really is.
But as I said before when calculating t-score we don't know true population parameters, in this case true population mean μ. So what number I should use in μ and how to calculate it?
An example, done a few ways
Assume for a moment that you ask that a pool of subjects estimate the price of something - say a new college textbook, for concreteness - and you're interested whether they over- or underestimate the true price.
Here you can look up the true price, so if it's 45 dollars and the price guesses are in dollars too, then the μ=45. If the subjects average guess is 60 then your t-test is testing whether there is enough evidence that they are systematically overestimating the price or whether their guesses could have have come from a population of subjects that neither under nor overestimated the textbook price.
Looking at this another completely equivalent way, you might subtract the true price from each subject's guess. Then you are looking at deviations from the correct price and the test would set μ=0 (unbiased price guessing)
Looked at a third way, you might think about running this test for all values of μ (you wouldn't really do this, but bear with me). For μs near the subjects' average, the test will 'not reject', but for μs quite far away from the subjects' average, the test will reject that the data came from a distribution with that value of μ. The region of μ values for which the test does not reject is, in a sense, the region of μ values that are 'reasonable' in the light of the data. This is one way to motivate the idea of (and sometimes actually construct) a confidence interval. When the confidence interval (the region of non-rejected μs) does not overlap 45 (or zero in the second formulation), then we reject the hypothesis that this population is unbiased in its textbook price guessing.
Each of these approaches get you to the same place in a different way. None of them require knowing the true value of μ. The first two are the ones to consider in your case.