Data protection legislation limits the use of personal data to that which is necessary. It would be difficult to justify a claim that your complaint cannot be considered without placing your name in the public domain. A complaint is a complaint, regardless of who voices it. Ask your Parish Council to remove your personal details or to justify, quoting data protection legislation, why it is necessary for you to be identified in this way.
For what it's worth, I take a mixed approach to this, often naming individuals in relation to good news stories, but never in relation to a complaint, either about the Council or another resident. It's sometimes easier to name than to find an appropriate form of words that avoids naming. When one of my Chairmen recently congratulated a resident on the award of a BEM in the Queen's New Year's honours list, she took the opportunity to address the Council in response. Not easy to minute without identifying her and, of course, the whole community already knew about her award anyway.