This name has pretty strong associations, and it would surely lead to teasing. It's better than the ugly Polly alone, but it's not a very pretty name. The name might lead to some credibility problems, and it sounds old-fashioned.
Pollyanna was a character in a children's book of the same name. She always played the glad game, where she would find something to be optimistic about even in the most negative situations. I think as a name it's quite pretty though it'd be odd to name a girl Pollyanna today, just because it's so old fashioned. The term takes on a more negative meaning though, meaning naively optimistic and moral. The Pollyanna character is sweet, kind-hearted and sympathetic and she teaches others to be optimistic which isn't a bad thing.
This name is not without teasing, especially considering that it means someone who's way too optimistic. It also looks pretentious and reminds me of a spoiled brat.
I've never heard such a name. It seems so fake... such an obvious combination of Polly and Anna! And it is difficult to pronounce. Much better name would be just Polina (or Pollina). Even Apolinaria would be better!