"Is a postdoc successful only when completed?"
Short answer: No!
Long answer: No it's not, mostly because there is no "completing" a postdoc, much like there is no "completion" in academia beyond the PhD unless you are going after a qualification for future promotion e.g. Habilitation in Germany (and possibly other German speaking countries?).
You are constantly accumulating information and experience, and there is no end to it as far as I can tell. There is always more to read, more avenues to explore, more projects to design, start and complete. Perpetual work...
There are people who spend less than a year as a postdoc and those that are practically stuck on a forever postdoc situation. When you leave your postdoc is a interplay of several variables:
- Availability of funds, or lack thereof
- How well suited you are to the research group and/or to the projects at hand (i.e. mutual satisfaction between yourself and your mentor)
- What other offers are on the table
- Any personal (e.g. family) constraints
I have never heard of a postdoc certificate, and would look very skeptically towards any such. That is not to say that it doesn't exist or that it wouldn't be legit just because I haven't seen or heard it, but it sounds extremely old fashioned and not really relevant anymore.
At the end of the day, when you write your CV you list your postdoc experience, over a given time period and what projects you have worked with during that period. When a potential employer looks at your CV carefully (in other words if they actually consider you) they might notice if the postdoc experience is too short, or if the projects listed there aren't published. As long as you can justify why you left a postdoc "too early" (whatever that may mean) you shouldn't have any problems
Hope that helps