Name of the psychological phenomenon of doing something just because you've already started doing it? I feel like people really often do things just because they've​ already started doing it.

One example could be the Electronic Evidence of Sales just established in Czechia. It's a system monitoring all the sales in the country by receiving electronic bills. Now, in order to launch it, every shop in the country had to buy a special cash register so we already invested a lot in it but some say it's ineffective so we should cancel it. And, of course, everyone says that would be dumb once we're using it but they don't realise that our past decisions are irrelevant for what we choose now, that is, a system with less effectivity. Note this story is just an example of a bad argument and might not be true.

The closest phenomenon I could find is the naturalistic fallacy and appeal to tradition fallacy. Among friends, I call it "the finishing syndrome", isn't there a more widely used term?
Although Cognitive Inertia (as mentioned by hexadecimal) is a nice, broad way to point to the phenomenon, people have also studied it from other points of view. Two of them are from economic and cognitive angles. 

From an economic level, what you are referring to is called the Sunk Cost Fallacy. Here is an example from Wikipedia that explains it from a business perspective: 


  In business, an example of sunk costs may be investment into a factory
  or research that now has a lower value or no value whatsoever. For
  example, \$20 million has been spent on building a power plant; the
  value at present is zero because it is incomplete (and no sale or
  recovery is feasible). The plant can be completed for an additional
  \$10 million, or abandoned and a different but equally valuable
  facility built for \$5 million. It should be obvious that abandonment
  and construction of the alternative facility is the more rational
  decision, even though it represents a total loss of the original
  expenditure—the original sum invested is a sunk cost. If
  decision-makers are irrational or have the wrong incentives, the
  completion of the project may be chosen. For example, politicians or
  managers may have more incentive to avoid the appearance of a total
  loss.




On a more personal level, this can be generally explained as the Zeigarnik effect, which states that "people remember uncompleted or interrupted tasks better than completed tasks".

Although there are some issues with the reliability of the effect, it is generally extrapolated to say that the phenomenon "compels humans to finish a task that they've already started, and that when we don't finish a task we experience discomfort and intrusive thoughts about it." (from an AsapSCIENCE video on "The science of Productivity")