What do you call someone who is always complaining after getting what they want? [duplicate]

I cannot find the precise word but there are many options which are close:

demanding - "making others work hard or meet high standards; not easily satisfied" (Oxford Dictionary)

misery - "a person who is constantly miserable or discontented" (Oxford Dictionary)

shrew - "an insulting word for a woman who always complains, argues, or nags."

fastidious - "hard to please."

high-maintenance - "demanding a lot of attention." (Oxford Dictionary)

ingrate - "an ungrateful person." (Oxford Dictionary)

There are some more options here: http://www.macmillandictionary.com/thesaurus-category/british/people-who-complain-a-lot-or-are-difficult-to-please

I would just go with the word "whiner." They whine when they don't get what they want, and they whine when they do.

What do you call someone when they're always asking for something,

You would call them a beggar.

and then is dissatisfied after getting exactly what they ask for?

Then you would call them a chooser.

This comes from the phrase "beggars can't be choosers".

TheFreeDictionary defines the phrase as:

If someone gives you something you asked for, you should not complain about what you get.

Wiktionary defines the phrase as:

When in need of help, one cannot dictate how that help is given. Put another way: when one's situation requires one to beg, one cannot complain about the insufficient or substandard gifts that one receives.