Where the names are the subject of the sentence, you'd better say:
"Danielle, Heather, Robbie and I" = He + He + She + I
People tend to say, " ....and me " but this is not grammatically correct.
If they are in place of an object, then you'd say:
Daneille invited Heather, Robbie and me
Subject + verb + object ( him, her and me )