If you dream of being separated from someone or of being left out, then you are processing through your feelings and attitudes about loss, rejection, loneliness, abandonment, autonomy and freedom. See Abandon or Break-up.
To dream of having separate identities suggests that you are feeling torn apart and divided. Your feelings are pulling you in opposite directions. You could also feel stuck between two people or groups in your life who want different things from you. You are feeling torn apart by this conflict - you must make a decision about the person who you want to become, and then act accordingly to make it happen.... My Dream Interpretation
To dream of a separation, or being separated (or kept apart) from somebody, symbolizes a real-life situation or relationship that is breaking apart. Or, this dream may also mean indicates that your feelings are pulling you in opposite directions in a waking situation.... My Dream Interpretation