In a stand mixer with a paddle attachment, mix the cream cheese until softened and fluffy.
Mix in the sour cream, mayonnaise, mustard, lemon juice, dill, and chives.
Add the salmon and artichoke hearts and mix until well combined.
MAKE AHEAD TIPS: You can make this dip up to 3 days in advance. Simply keep the dip in an airtight container. If you use a bread bowl as I did, transfer from the airtight to container to the bread bowl just before serving. MAKE THIS DAIRY-FREE: Substitute your favorite dairy-free cream cheese and dairy-free sour cream for regular cream cheese and sour cream.