Connotation already had an established usage before logicians ever used it; and that usage is both very different from and used in the same very specific area of discourse as this new definition. If definitions were trademarks, this would be a violation.

You're using 'new' in an interesting way here. This usage of 'connotation' was arguably first taken up by Mill in 1829. The word 'connotation' was first used by logicians in the 17th century, though it tended to mean something more like "the proper category to put something in", and Mill was explaining he'd like to use the word more sensibly than that. The 'common usage' you refer to was possibly a bit earlier, 16th century if I'm to believe OED. And it was not a term of art.