Ideally internet-connection would be about connecting to the Internet or troubleshooting connectivity and performance problems. The internet tag is of course far broader.
If people don't tend to use the internet-connection tag in a way that's different from internet, we may as well merge them as proposed.
I'm not sure that's what's going on, though. Most of internet-connection questions seem to fit within the narrow scope of connectivity issues.
I recommend keeping internet-connection, at least for the time being. As for the connection tag, though, we should really get rid of that (by retagging its questions). There isn't anything practically similar about connecting to the Internet and connecting a USB mouse. The "connection" concept is too broad for a tag.
connectiontag, which covers internet connections already.