There is no problem.
I'm from outside the States and had no idea the two weren't the same thing. And even when I would have known the difference, I would've come to this SE site to ask questions about electronics.
From an SEO (Search Engine Optimalisation) point of view, I'd say this name is really good. We have "Electrical Engineering" as a name, but "electronics" in the URL. That makes this site score high in search engines, both on queries with "electrical" and on queries with "electronics".
Name changes aren't nice
Not only because 'we're used to electrical engineering', but also because of the search engines. They'll have to get used to the new name, crawl all pages again, et cetera, et cetera. You really don't want to have two different names wandering around the net. In the end, the search engines will get used to the new name though, so this is merely a temporary problem.
The description says it all
We should ward for descriptions in titles. For example, "This is my homepage about blah", isn't a good title, it's a description. The title should've been either "My homepage" (though it doesn't say a lot) or "Blah".
EE's description on our FAQ (and stackexchange.com/sites as well) says:
Q&A for electronics and electrical engineering professionals, students, and enthusiast (...) which include electronics, physical computing, and those working with microcontrollers, Arduinos and embedded systems.
That's a very good description and I think anyone can agree with that. We should ward to put the description of the site in the title. We do not want a title like "Electrical and electronics engineering, and a bit about electromagnetic forces and communication schemes as well".
We have a logo
And apart from the title and the description, the logo (and the overall site design) is a good way to profile your website. Our logo is more electronics than electrical engineering:
... and thereby shows everyone that electronics is included in the scope of this site. Also the overall site design, with chips, LEDs and a breadboard, is more of electronics than of electrical engineering.
"Electronics" is confusing
As stated in Possible Name Change?, the word "Electronics" is associated with consumer electronics. This question shows there was a problem with the word "Electronics", and even now, I think we have too much questions about consumer electronics. We really don't want more, do we?
I don't think we should have a name change.
I will be reading this question and its answers with great interest to see with what you come up.