What type of bonsai tree is this and why is it losing leaves?

I think You'll find that it's a Chinese Elm (Ulmus parvifolia) The Zelkova or Japanese Elm has slightly pointier leaves... although this is merely from observing your photo!

Location changes can effect your bonsai along with changes in lighting, temperatures, watering schedules and fertilizing can stress a tree. The way they show you that they are stressed is by shedding leaves, usually they'll turn yellow first but not always.

However the Chinese Elms are very resiliant trees and can recover better than most other species with a little care.

Keep the tree next to a light source ideally a south or west facing window (early morning or evening sunlight is best as it's not so harsh) but sunlight is very important!

Water as required not daily, weekly or to any schedule. Make sure not to over water it remember roots need oxygen or like us they will suffocate. Make sure the soil is damp not sodden or the roots will rot (this is a slow killer)! Water only when the soil starts to dry below the surface you can check this by pushing the tip of your finger about a centimeter into the soil (or get a fairly cheap water meter), if it's dry then water if damp repeat the process the next day and so on... from the picture you posted it looks like you have a water retentive soil so remember not to over water!

If the tree recovers well enough think about repotting it with a free draining soil (In early spring as the buds swell, And never a sick or stressed out tree if you can avoid it)... Chinese Elms will grow in almost any medium but at least this will mean you're less likely to overwater them!

Finally fertilizing a stressed out tree is a sure way to make it worse let it settle into it's new surroundings it'll tell you when it's happy with new buds bursting all over then fertilize, once every 2 weeks in the growing season which is March through to the end of September here in the UK, with a good bonsai fertiliser (it's good practice to just give the tree a watering prior to fertilizing as this prevents the fertilizer burning the fine roots if they are dry)!

Just as a pointer although most people enjoy the thought of having bonsai trees as house plants, Chinese Elms are trees and as such thrive outside in the natural environment. I've grown them indoors and outdoors and although they are one of a few species that can survive indoors, they will never grow as well as their outdoor counterparts with both health and vigour. Unless that is you can recreate their ideal micro climate indoors.

Fingers crossed your bonsai settles in and grows well. Good news is that from your photo it looks like there is fresh growth, so don't panic or fuss over it too much or it'll continue to stress out, keep a watchful eye on it and tend to it as and when it's needed. It'll do the rest, as mentioned before they are one of the more forgiving bonsais and do bounce back.

Remember in bonsai you will inevitably kill a few trees the trick is to learn from this and if you enjoy it keep going! It's well worth it. Good luck!

This looks like Zelkova, here a close up of the leaves, I had one for years. It was sold as an indoor bonsai, but my own experience was that it was better off outdoors (in Netherlands). However, you must protect it from frost of course. This species, Zelkova, sheds its leaves when stressed, but most of the times it will recover when the stress is gone. So it will get back its leaves. I found it a very resilient (or forgiving) plant, it came back from a stressed state many a time. The stress your plant is experiencing now could be due to the movement to your new place. It can be that it has lower light levels there or different moisture levels (those two factors are in my opinion most crucial).

So my own experience is that it is better to keep it outdoors (get it indoors with frost). I had one for years, but eventually it died during a hot summer.

Your Bonsai appears to be a type of Elm tree, Ulmus parvifolia, or an Ulmus parvifolia Cultivar or hybrid; close illustrations of several leaves and branches could be helpful in identification. Also, if convenient, might be effective to go where it was purchased and see if there is a Bonsai like yours that has a name tag, or perhaps try otherwise contact the place and enquire of the species/ cultivar name, and also enquire of your tree's history, the soil it's in, age etc.

From the illustration, the new leaves look healthy, which is a good sign, and several of them should grow a bit larger. It looks like it may need more light, the lack of which could be bringing on some of the difficulty, along with the colder environment. And may be too wet: the soil doesn't look just so, and the tree may need to be reset if it was recently simply placed in the container for sale. The soil should be specialised for that type of tree, compared to vegetable soil, and there should be some coarse material in the bottom and a hole or holes in the bottom for good drainage and aereation. A closer up illustration of the base and center could help advise more effectively. It looks like it could use some trimming, but if it's ailing that isn't the time to do it unless circumstances are extreme.

The watering should be such that it doesn't become dry, but doesn't remain wet: it should have adequate drainage. Wouldn't suggest adding any nutrient at this time, since your tree is doing sort of unrobustly. If there's decomposing leaf material gently remove that, And check very closely for any sorts of bugs: a few little bugs can rapidly mess up a little tree! If find any, maybe try very carefully remove them manually, but be very thorough!

Maybe try getting it more light & watching the water, and check on it fairly often. Your Bonsai looks fairly well established and has nice form!