BDD is a way of developing, just like TDD (albeit typically at a more abstract level). Frameworks like JBehave and Cucumber can aid you in your behaviour driven development.
Labelling arbitrary tests ‘BDD tests’ just because you used a given/when/then syntax, completely misses the point of BDD – and devalues any real BDD that you might be doing.
And finally, as an aside, if you value your ‘BDD tests’ for any living specification they offer – then that living specification is precious! Don’t ruin it with tests which don’t serve that function in a clear and concise manner. Especially if the only reason you’re adding those tests is because ‘we do BDD’.