Yes, this can have a psychological basis, and it’s actually quite understandable given what you went through. Trauma, like rape, can trigger very intense emotional and psychological responses. Getting your mom’s name tattooed could be connected to several underlying factors:

1. Seeking Safety and Protection: After a traumatic event, people often crave feelings of safety and security. Your mother might symbolize protection, comfort, and unconditional love. The tattoo could have been a way of carrying a sense of safety with you permanently.
2. Emotional Anchoring: Trauma can make you feel disconnected from your body or your sense of self. Tattoos can serve as an anchor to something stable and familiar. Your mom’s name may have represented an emotional anchor during a time of extreme vulnerability.
3. Commemoration or Connection: You might have wanted a permanent reminder of someone who loves you and stands by you—a way to feel connected to your mother even if the trauma made you feel isolated or unsafe.
4. Control Over Your Body: After rape, the sense of control over your body is often shattered. Choosing a tattoo is a way of reclaiming ownership and expressing control over your body, even if only symbolically.
5. Psychological Coping: Trauma can manifest in symbolic acts like tattoos. Your choice could reflect an attempt to cope, process, or communicate your inner feelings when words alone might not have sufficed.

In short, yes—it’s very much psychological. It’s a symbolic act of seeking comfort, connection, and control in the aftermath of something that left you feeling powerless.