double room capacity

I am booking Double Room with Small Double Bed, Can it Fit 2 person?

If I booked double room with small bed for 1 person. Can I add extra person on the day of check in?

You need to ask the hotel.

A small double is simply a wide single. Yes, it can fit two adults, but something I personally wouldn't do if I wanted a good night sleep.
Changing from a single person to a double booking at check-in will present you with issues like a different room rate or even denyed accommodation for the second person (hotels in Japan have very strick rules about the number of people in rooms and the hotel), so there is no guarantee an extra person can be added on the spot. At a minimum, expect to pay more, and if you did your booking through an agent/discount website, expect to pay potentially full price for two.

Re. bed size - some hotels will tell you the dimensions of the beds on their websites.

I've seen the term "semi-double" used on Japanese hotel sites in the past, and have booked them several times. Whilst significantly narrower than a US King-size, my experience is that they're fine for two people the odd night here and there...assuming that your relationship with the other person is such that you're happy being cosy with them.

I am booking Double Room with Small Double Bed, Can it Fit 2 person?

The size of the bed differs greatly depending on each hotel or room. You need to ask if you want to know the size. Some hotels might have the size written in their website.

By the way, I know a lot of people, of various race, nationality and size, who have slept in the tiniest single-size beds on a daily basis. Whether you "fit" depends on your preference.

If I booked double room with small bed for 1 person. Can I add extra person on the day of check in?

If it says that the room is for 2 people, you can by paying an extra fee. But if it's a room designed for only 1 person, you cannot, because the fire safety law does not allow it. By the way, a "single room" is for 1 person only.

I hope it helps.