Can overfitting happen if I have number of data points that way more than number of features? In most cases, more parameters in the model, more data is needed. 
My question is: can overfitting happen if I have number of data points that way more than number of features (for example, the design matrix is $10K \times 10$) ?
 A: Theoretically, yes.
Having a model that is large enough to memorize the data and provides predictions based on that instead of discovering patterns in those ten features would be an example. In the end, it is rather a relation between model size and size of the data (in terms of number of samples and complexity of the data space), and of course the exact algorithm and learning problem at hand.
An extreme case where the problem would disappear is when you had so vast amount of data that it actually covers the whole data space, in which case overfitting to that dataset would mean having a perfect model, since it knows the answer to every datapoint. If the ten features were binary, 1024 samples would be enough.
A: A couple of more considerations:


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*there maybe duplicate data (can happen in real datasets), in which $10K$ doesn't mean a lot and overfitting can be relatively easy.

*Independent of your data, a decision model memorizing the samples is overfitting. For example, decision trees can be though as a bunch of if-else statements (trained via some method). So, if one can provide $10K$ if-else statements after looking at your data, it'll basically be an overfit.
