It's hard to tell from the photos what size it is but I'm guessing about 50cm? Which is a bit on the small side. The RSPCA used to have some recommended minimum sizes, which people tend to go by. For a Syrian it was at least 80cm by 50cm. For a single dwarf hamster it was 70cm by 40cm and for a pair of dwarf hamsters, the same as for a Syrian 80cm by 50cm. As Cypher says, a very large cage doesn't always work for a pair of dwarf hamsters, but it does need to be big enough to fit two of everything inside, and that is really important when you have a pair. So two houses, two wheels, two food bowls, two water bottles - and no shelves or levels (shelves can encourage one to get territorial). Houses ideally with two entrances. And still have enough floor space for them to run around and dig in. Even to the point of not handling one more than the other or giving one out of cage time more than the other.
Keeping a pair is lovely but many people end up having to separate them due to fighting - and they can seriously maim or kill if fighting starts. They may be ok at first, but as they get older and hormones kick in, falling out gets more likely. Also a pair needs to be siblings - either two brothers or two sisters. And many people, unfortunately, get sold a pair who have been sexed incorrectly and end up with babies - which means a lot more cages to find, before you can find homes for the babies. So it is something to be considered very carefully and with plenty of research.
I would suggest if you haven't had dwarf hamsters before it would be best to just get one. Depending on the actual size of that cage, it might be ok for one dwarf hamster, but you might need to upgrade it if you get a dwarf hamster who needs more space - they do vary in personality.
It's fine keeping them in the same room. One thing that hamsters don't handle well though, is having their environment changed - eg moving the cage to a different room or even a different location in the same room - this can trigger a lot of stress behaviours. So best to leave a cage where it is, once a hamster has settled in. So if you get a new cage for your Syrian, ideally put it in the same place as the old cage was. Then find somewhere to put the smaller cage if you're getting a dwarf hammy.
It might be an idea to hang fire and just get the Syrian settled and tamed first
Your old cage can be very useful. As somewhere to put the Syrian when you need to do a cage clean (eg as a play cage), or as a holiday cage, if you ever need to take your hamster with you if you go on holiday - it is something small enough to transport with you and ok for a week or so if set up with familiar things from the main cage.