We have various translations for "to have". It's very dofficult for me to explain about it without using Japanese sentence. Please review this when you can read them and understand them.
By the way, please don't separate もって and いる because IN THIS CASE, もっている means "to have". In my opinion, remembering the translation もっている for "to have" for "to own objects" would be better. Please remember that there are cases that each words don't have the specific translation and each language has its own way of saying.
Anyways, here are the basic and most common examples.
"To have" for the person, we say いる/います.
I have a younger sister. = 私には妹が一人います。(わたしにはいもうとがひとりいます。)
I have many friends. = 私にはたくさんの友だちがいます。(わたしにはたくさんのともだちがいます。)
For pets, we say 飼っています(かっています).
I have dogs. = 私は犬を飼っています。(わたしはいぬをかっています。)
For the object, we say もっています like "to own".
I have a book. = 私は本を持っています。(わたしはほんをもっています。)
Like "there is/are", we say ある / あります.
My city has a big park. (There is a big park in my city.) = 私の町には大きい公園があります。(わたしのまちにはおおきいこうえんがあります。)
Other example:
May I have your name? (Please tell me your name.) = おなまえをおしえてください。
Please get accustomed to the Japanese language step by step. I hope this was helpful.