In today’s globalized world, technology-mediated communication aims to enhance social presence and connectedness for people who are acquainted, but spatially separated. Avatar research is concerned with optimizing the visual and functional representation of people in virtual reality (VR) to bridge spatial distance. VR immerses users but does not allow for shared experience of events in real environments. This problem is addressed by using telepresence robots (TPRs). Virtually extended telepresence creates highly immersive experiences for TPR drivers while they participate in the local environment of their acquaintances. Representing TPR drivers by personalized avatars on TPR screens mitigates the challenge of drivers’ eyes being covered by VR devices. However, avatar research rarely includes acquaintances. Therefore, it is unclear whether avatars add value, as the perception of familiar voices may be sufficient for high social presence. A study was conducted to investigate the effects of a familiar voice and avatar representation separately. 29 participants played the well-known game Tic-Tac-Toe in a virtual environment against an experimenter they knew personally. Study design followed a 2 × 3 mixed-design with the possibility of voice communication (non-verbal vs. verbal) as a between-subjects variable and avatar representation (none vs. standard robotic vs. personalized humanoid) as a within-subjects variable. Results showed main effects of both independent variables on social presence, person recognition and social connectedness. Combining voice with personalized avatars showed superiority for outcome criteria. Therefore, personalized avatars show great potential to enhance social connectedness in virtually extended telepresence. Design recommendations for both the private and professional context are given.