Should we add the name of the identified series to the list of tags for identifications questions with accepted answers? Would it have any significant impact on SEO?
Others have addressed the whole "Tags identify attributes of the question" already, so let me piggy-back a bit on the point from Gilles.
Certainly, having a tag in the title will increase searchability... based on including that tag's content in the search string. Which is where the logic of its benefit is starting to fall into a logic gap for me.
The entire class of question is based on the premise that the title is an unknown element - that's the whole purpose behind asking the question. Furthermore, it is knowledge of the title which is, entirely, the solution to the problem at hand. Thus, knowing the title invalidates the need to ask the question entirely.
Adding the solution to the searchability means that we increase the visibility of... nothing. The question is of absolutely no use to those who already know what the name of the series is, by virtue of the fact that the sole and complete contribution of the solution is the name of the series. The people who can search for the title gain absolutely no benefit to finding this content, since this will not be a problem they are searching for. If anything, it may even be problematic as this will turn up as a search result for unrelated inquiries they happen to be asking about the series itself, giving them worthless data.
To those who do have the same problem, it provides no benefit. They cannot take advantage of the increased searchability because they don't know the title that they can use to help locate the question.
Internal to the system and stepping out of the Google search implications, tags serve to identify what the problem is about, so that questioners can find people with the same problem, and that answerers can identify places that their expertise is needed. There is a difference between "What a problem is about", and "What a problem is solved by" - especially since the latter may have more than one component. This is why we only tag based on the former concept - if we tagged on every potential solution to each problem, then tags would be bloated with excess information that makes finding things more difficult. To further in this point, tags are only an attribute to the question, not to its answers, and thus the logic of tying a tag to its question is written into the system.
For programmers, a Stack Overflow style example of this argument can be found here. It can be read on a more general component even if you're not a programmer, but if you don't feel like breezing through that, that's fine.
Think outside the context of identification, and put aside the issue of tag granularity for this example - a problem about how to shoot Gohma in the eye when her claw is blocking it is fundamentally different from a problem about how to open the door to Undine's lair, which involves shooting a statue in plain sight in the eye. That they both involve shooting things in the eye does not cause the latter to be grouped with the former on the grounds of shooting things in the eye, because the latter is not a question about shooting things in the eye, but about accessing lairs. You would not tag the latter question with a tag about shooting things in the eye. If there was an alternate entrance to Undine's lair involving bombing cracked walls, then that makes a tag about shooting things in the eye even less applicable because it may not even be necessary. Arrows will be the optimal solution because bombs are extremely expensive and heavy, and thus that is the accepted answer, but that still doesn't make it a component for the tagging. Tagging it as such would only make the whole system confusing.
To use a less confounding example, if that was hard to follow, if someone needs to accomplish Task X, and the solution, wholly and straightforward, is to use Strategy Y, then this is not a problem that is about Strategy Y. We would not classify Task X under Strategy Y because people who are looking for problems about Strategy Y would not be looking for Task X - Task X is already a solved problem for them by virtue of them knowing Strategy Y. We especially would not classify Task X under Strategy Y if there was also a Strategy Z that was equally capable of accomplishing Task X. Then Strategy Y isn't even necessary for Task X, and people who are seeking Task X wouldn't know to search for Strategy Y (or Strategy Z). Had they known to search for those, they probably wouldn't need to ask about Task X in the first place.
That's rather the whole of it. The searchability benefits don't really manifest to anyone's favor as they don't increase visibility to those who would need to find it. Questioners won't know to look for the series as that is the item they are wholly seeking. Answerers won't look for the series because seeing that present is a clear sign that their help isn't even needed.
If you're asking whether we should add tags with the series to identification questions, then the answer is no, this is as far as I know the usual practice on the SE sites.
Tags should classify questions, not questions-after-they-have-been-answered. If the OP didn't know it was that series, then you should not add the tag. It would make the question silly (the asker doesn't know the series but the tag is there).
The keywords in the answers are enough.
Answering to comments: First of all the fact that tags appear in the question. Answers do not carry tags, so tagging a question according to its answers has no logic. Second, the tags appearing on a question, classify it: what it's about, etc. But the OP cannot tag something which he's asking. Consider this: if a user asks about a proper sentence in a language and his example has a mistake, do you fix his mistake in the question? No, because then the question would not make sense anymore.
As you mentioned, it will help with Search Engine Optimization (SEO).
Furthermore, it lets you find all the identification-request questions associated with a specific series.