Tip:You can mix the cream cheese up to one day ahead and refrigerate it in an airtight container. Bring it to room temperature before using. The rolls can be assembled, covered, and refrigerated up to 4 hours ahead. Let stand at room temperature for about 15 minutes before serving.
In a small bowl, mix the cream cheese, lemon juice, zest, chives, and 1/8 tsp. salt.
To assemble, lay an 8 or 9-inch long sheet of plastic wrap on the counter. Slightly overlap slices of salmon on the plastic to create a rectangle measuring about 3-1/2x7 inches. The long side of the rectangle should be parallel to the edge of your work surface. Cover with another sheet of plastic and press gently with your hands or a flat spatula to encourage the salmon to stick together. Remove the top sheet of plastic. Using a thin metal offset spatula or a butter knife, spread about 2 Tbs. of the cream cheese mixture on the salmon, leaving a 1/2-inch border along the long sides. Arrange about a third of the fennel shavings lengthwise on the lower half of the salmon. Sprinkle the fennel lightly with salt. Starting at the long side closest to you and using the plastic wrap as an aid, gently roll up the salmon to enclose the filling. Gently press the roll together at the seams. Transfer the roll to a cutting board. Cut the roll into 6 pieces. Repeat with the remaining salmon, cream cheese mixture, and fennel to make 2 more rolls. You may have extra salmon or fennel.
Arrange the rolls on a platter, cut side up. Garnish with the chopped fennel fronds.