We already have phrase-requests for users searching for multi-word expressions, so a rename is not in order. The tag single-word-requests really is (supposed to be) about single words, and that should be taken into account when writing an answer to a question with this tag. (Questions may be tagged with both to emphasize that either a single word or a multi-word phrase would serve.)
If you see a multi-word response to a question tagged only with single-word-requests and not with phrase-requests, and it looks like a good answer aside from this, the first step I'd advise is making sure that the original poster really wants a single word.
The simplest way to find out is if the original poster actually says something about a "single word" in the question, title or comments. (Many of these questions ask for "a word" or "the word" for something, but this wording is somewhat less clear, and might potentially encompass a multi-word phrase.) And on the other hand, the original poster might say somewhere that they would accept a multi-word phrase.
If the original poster hasn't made it totally clear in their writing, I would then check the history of the post to see if the single-word-requests tag was on the question from the beginning, or if it was added later by an editor. (For an example of the latter, look at the history of this question.) If the tag was added later, and the original poster only used vague terminology like "what is the word" or "give me a word," I personally wouldn't consider this evidence enough that only a single word is strictly acceptable. In this case, you might want to leave a comment below the question asking the original poster for clarification.
All of the above is basically to remind you that it's possible that the mistake is not in the answer, but the tag. In that case, a downvote for this reason would clearly be inappropriate; the tag should be changed.
But what if it's clear that the tag is correctly applied? It is up to you how to use downvotes. Personally, I would generally not downvote answers that are good aside from this issue. Such answers are in my opinion useful, even if problematic, because people who find the question later might not have such stringent requirements.
In some cases, even when the OP explicitly says they want a single word, they end up going with a phrase. See this question, where the questioner talks about a "single word", but the accepted answer ended up being a two-word phrase.