We have three tags related to the "When they Cry" franchise: when-they-cry, higurashi-no-naku-koro-ni, and umineko-no-naku-koro-ni. Are all three of these necessary? And if not, which should we keep, and what synonyms should we use?
In my opinion we do not need all three tags.
There is very little in common between Higurashi and Umineko. The characters are almost entirely different, and the plots are basically unrelated. Almost all the in-universe questions that make sense to ask are specific to one or the other. Plenty of people (including to some degree myself) are an expert on one but not the other. Wikipedia doesn't even have a real entry for the series; what they have is a disambiguation page pointing to Higurashi and Umineko. Hence, we should probably have different tags for the two.
As for whether we need a third tag for the series as a whole, this seems unnecessary right now. It's not prohibitive to just use tags for both Higurashi and Umineko for the few questions about the series as a whole. More importantly, this tag risks being used on questions which are specific to one or the other, like What exactly are the rollbacks in Higurashi?. If that happens, this tag will be the most used, which will be bad for SEO since "Higurashi" and "Umineko" are likely to be the most common search terms. If the franchise expands significantly it might eventually be necessary, but for now such a tag is counterproductive and harmful to SEO.
As for what tags to use, all things being equal we should prefer the English language version of the names. The most common search terms are just "Higurashi" and "Umineko" which will be caught by either the English or Japanese titles. Hence we should use higurashi-when-they-cry and umineko-when-they-cry. Synonyms should be made for the Japanese names higurashi-no-naku-koro-ni and umineko-no-naku-koro-ni.
Keep all three tags.
- higurashi-no-naku-koro-ni is specific to Higurashi (WTC1-2)
- umineko-no-naku-koro-ni is specific to Umineko (WTC3-4)
- when-they-cry is for overlapping parts of the franchise
The Umineko sound novels provide some further insight into the workings of some parts of Higurashi, and therefore What exactly are the rollbacks in Higurashi? probably could not be explained fully without knowledge gained from Umineko, despite it being a question about Higurashi. This is why it is tagged when-they-cry - this is a question about overlapping parts of the franchise.
If they are so unrelated as Logan M's answer claims, then why has the creator given them not only similar Japanese titles but also series-like English titles?
Not sure if this is worth nothing, but it is rumored that WTC5 is in the works to some degree already.