I named him siggy, and mom didn't like it..

You can name your dog whatever you want screw what other people think.

It's not much of a difference.

One cat we named Indie but call pouf. One is Jamie but I call her Jameson. One is tullamore but we call her Trogdore. And one is snookie but we call her floof. Lol.

Yes, I’m a crazy cat lady. And having more than one name for anyone or anything is normal.

It is the same thing, sziggy.

Ziggy reminds me of quantum leap.
Either way if you named your doggo Siggy why would you tell people their name is Ziggy?

Amen to the cigarette point and also Ziggy is David Bowie's nickname.

Fuck your mom. In fact, I did last night, but that's beside the point.

The dog's name is Siggy. Does your mom own the dog? No, you own the dog. Thus, tell people the name is Siggy, and explain the situation if they thought it was Ziggy. Any reasonable person would call him Siggy, seeing that's what you named him.

The issue is probably that "Siggy" could be mistaken as slang for "cigarette", which is not exactly the greatest thing to name your dog.