Do other forms of bias have their own terminologies, similar to "Stockholm Syndrome"? Three examples would be:

Someone who makes an expensive purchase, and even when they are met with objective facts stating why it was a inferior purchase, they continue to sing it's praise.  

Someone who blindly follows and defends their political party affiliation, even when confronted with facts showing why it's a bad affiliation.

Someone who commits to a lifestyle choice, and even when confronted with facts showing why it's a bad choice, they refused to believe it.

I know an all encompassing term might be cognitive bias, but I was hoping for specific terminologies to the three types of biases above.
Yes, Wikipedia even has a list.

Someone who makes an expensive purchase, and even when they are met with objective facts stating why it was a inferior purchase, they continue to sing it's praise.

This is related to the endowment effect and sunk costs fallacy.

Someone who blindly follows and defends their political party affiliation, even when confronted with facts showing why it's a bad affiliation.
Someone who commits to a lifestyle choice, and even when confronted with facts showing why it's a bad choice, they refused to believe it.

These are both fairly closely related, and there are several types of bias that could contribute to either - you'd have to have more information about what led to that bias, as you are sort of describing the 'symptoms' rather than causes. Conservativism bias, confirmation bias, bandwagon effects, social comparison biases, selective perception, reactance, and more.
However, I would also encourage you to be wary of the many forms of bias that cloud your judgment of others, as well. If you are perceiving people as being part of a 'bad affiliation' or making a 'bad choice' you should consider that your own biases may cause you to discount the reasons for those decisions. You may value different things than they do, and those differences in values may or may not be related to cognitive bias per se, but also simply individual differences in personality, life experience, etc.