Although there is a potential demand for customizing voices, most customization is limited to the visual appearance of a figure (e.g., avatars). To better understand the users' need, we first conducted an online survey with 104 participants. Then we conducted a semi-structured interview with a prototype with 14 participants to identify design considerations for supporting voice customization. The results show that there is a desire for voice customization especially for non-face-to-face conversations with someone unfamiliar. In addition, the findings revealed that different voices are favored for different contexts from a better version of one's own voice for improving delivery to a completely different voice for securing identity. As future work, we plan to extend this study by investigating voice synthesis techniques for end-users who wish to design their own voices for various contexts.