We have present-perfect-tense alongside past-perfect,future-perfect, perfect and simple-past. However, present-perfect does exist as a redirect. I think it would be better to make it the main tag, which would be more consistent. Some might also consider it more technically accurate, since the present perfect is generally described as a combination of tense and aspect.
Note: The answer to the following meta post suggests using the word "tense" in all of these tags, but the post is quite old and it looks like that suggestion was never implemented: Which should the tags for tenses be? In addition, the question talks about "past-tense and future-tense," which it does seem might have some ambiguity as single words; but "present-perfect" seems completely unambiguous to me as it is. The answer there even calls it a "problem" that "tags like present-perfect-tense are rather long."
In any case, I have now posted an answer there, so please upvote it if you agree with me and disagree with the older answer.
Edit Oct 1, 2015. There hasn't been as much community discussion as I would like, either below this question or below the linked question. However, there have been 11 upvotes, and there was only one downvote, and the post has been up for nearly a week. This indicates to me that the community is in favor of making this change, so I'm going to try to actually get it done now. According to this question on Meta SE: How to rename a tag?, a moderator should be able to do this, although I'm not sure if the issue is complicated by the fact that the two tags are already marked as synonyms of each other. I'll ask a moderator in chat and see what happens—if more community action is needed (for example, voting on tag synonyms) I'll post about it here.