Yes, there is a word for “have” in Japanese. However, it is doesn’t have just the meaning of “have” like our English word does, and that is why people get confused. To begin with, they have the word “mochimasu” which means “hold.” “motsu” = “to hold.” That is often used for “have,” but we have a meaning in English for “have” that doesn’t mean “hold.” For that meaning of “have,” the Japanese use the verb “arimasu.” Yes, “arimasu” also means “is, am, are, and will be.” However, it can also mean “have, has, there is, there are, will have, and there will be.” You see, they have “desu” which means “is, am, and are,” and that is all it means. “Arimasu” carries a larger meaning than beginning students of Japanese realize, and there is another word like it: “imasu.”
Japanese also has another word along these lines that the beginning students may not know or realize is there. That word is “imasu.” “Imasu” is the same as “arimasu,” but it is talking about people. I can say “hako ga arimasu” for “There is a box,” “I have a box,” “There will be a box,” “There are boxes,” “I will have a box,” “He has a box,” “She has a box,” “It has a box,” and “He will have a box,” etc. However, if I want to talk about a person or people, I can’t say “Hito ga arimsu.” It is wrong. I have to say, “Hito ga imasu” meaning, “There is a person” or “He has a person” or “She has a person” or even “We have” or “They have a person.”
You have to get used to words and concepts not translating directly though when you speak a foreign language. Often times, there is not specific translation for what you want to say, so you approximate it. Translation is not a Science. To speak a foreign language, you must know the grammar, but even grammar doesn’t translate exactly. Speaking a foreign language takes someone who can understand hard and fast facts, but then be creative with those hard and fast facts. Speaking a foreign language, in many ways takes the ability to understand something that is supposed to have a lot of order like Math, but then you must also have the ability to be creative and put it together like art.