I realize that in popular culture, Satan, Lucifer, and The Devil are synonyms, but on a more theological level, they have distinct meanings, which may overlap to varying degrees, and in some belief systems, aren't even synonymous at all.
Is it appropriate that the tags then are synonymous?
I noticed it with this question: What is the Biblical basis for saying Lucifer is an angel?
It should be tagged lucifer for sure, as it's clearly about that. But it's not (necessarily, depending on one's theological framework) about Satan or The Devil--and whether it is or not, is irrelevant to the specific question at hand.
So I'd be in favor of splitting the synonym in this case.
On the other hand, I can see a lot of room for mis-use of these tags, with people tagging every question about "Satan" as all three lucifer, satan, and devil, or perhaps worse, one of these, randomly.