I fill these out all the time. "They" already know you own guns, they're not supposed to but they keep track. I gave up worrying about such things last year. They know everything about us and it's all stored in a computer and literally can be accessed in seconds. So like I said I stopped carrying about it, joined the ISRA and the NRA and made it official.
Now I proudly put my name on as many of these surveys as I can find. But I don't think anyone would know if you said your name was "Tim Smith".