Protocells are objects that mimic one or several functions of biological cells and may be embodied as solid particles, lipid vesicles, or droplets. Our work is based on using decanol droplets in an aqueous solution of sodium decanoate in the presence of salt. A decanol droplet under such conditions bears many qualitative similarities with living cells, such as the ability to move chemotactically, divide and fuse, or change its shape. This article focuses on the description of a shape-changing process induced by the evaporation of water from the decanoate solution. Under these conditions, the droplets perform complex shape changes, whereby the originally round decanol droplets grow into branching patterns and mimic the growth of appendages in bacteria or axon growth of neuronal cells. We report two outcomes: (i) the morphological changes are reversible, and (ii) multiple protocells avoid contact between each other during the morphological transformation. The importance of these morphological changes in the context of artificial life are discussed.