Is it permissible to place intellectual property rights (such as a website name or address) on visual and audio materials and websites designed for the sake of Allah Almighty, and does this affect the reward and recompense?

It is permissible to retain the rights to audio and visual materials, whether for yourself or for the website, and to write your name or your website's name on designs. This is because the purpose is to prevent commercial copying, not personal copying, and to attribute the materials to you to prevent their usurpation. This is permissible and rewarded according to your intention. However, if you dedicate them to all Muslims without retaining any rights, whether for commercial or personal use, and do not write your name on them, your reward and recompense will be greater, it will be further from ostentation and seeking fame, and closer to sincerity, as Imam Shafi'i, may Allah have mercy on him, wished.