We aren't the only SE site not named exactly for its topic. I know it's one of the more obscure sites, but ahem, Stack Overflow. There's also Super User, Server Fault, Arqade, Android Enthusiasts, Database Administrators, Programmers, Writers, et. al. What evidence is there that the name is a problem?
Changing our "brand" isn't going to do anything without a corresponding campaign to re-market the site and explain why we're changing the name and drum up some business. Maybe before we make a such a big change, we should get off our butts and make some community promotion ads for EL&U (https://english.meta.stackexchange.com/a/7628/80039)
My impression is that most folks don't find us by searching for the name; they find us by searching for an answer to a question. I think that if we work on our questions so that they come up near the top of the first page of an Internet search for the same sort of question, that would have a much bigger impact than changing our name. I think our non-native speakers could really help us with this, because they will have some insight into what search terms a learner might use. Does the text of the tags on a question get indexed by search engines I wonder? That might change my opinion of whether we should keep certain tags around.
There is a lot of overlap between the EL&U and ELL communities, but from what I've seen, the EL&U folks are migrating over appropriate questions. If there is a problem that I'm not aware of, I don't think changing the name of the site is the solution we should try first.