Despite the company's clear origins and meaning behind its name, a rumour began that the name "Gap" was an acronym for "Gay and Proud". This rumour is unfounded and has been debunked by sources such as Snopes.
To answer the question directly: yes, you can be gay in Fallout 4. The game features a same-sex romance option for the male player character, and the game’s writing and dialogue are inclusive of the LGBTQ+ community.
Apurva Asrani is one of the few directors in India who is openly gay Source: Shonali Bose. Indian film director, writer, and film producer Shonali Bose identify herself as a bi.