If they are miniatures the leaf and bloom size will not get larger. Although, the plant will grow. I know they state 8 to 12 inches but miniature rose plants can get as large as 3 feet tall. And if it's a climber it can go 10 to 12 feet high but will still have those smaller blooms on it.

Be very careful when separating the roots so you do as little damage to them as possible. Plant them in well draining pots with a good quality potting soil until they get to a large enough size to plant them outside. Roses do not do well in the conditions inside the house and much prefer being outdoors.

As for the names, if they came with any kind of tags there should be a patent number somewhere on there that you can look up. If not the growers name might lead you to who the breeder is and most of them have web sites where you can try and ID them from pictures. It's not always easy to do though because many of them look alike and they have a bad habit of switching out different roses for the same name.

To answer your question accurately, Queenbee, you can't. Some are "dwarfed" by being grown in small pots. Some may actually be sprayed with growth hormones to inhibit their size. "Miniature" means bloom size. Some may develop into five foot plants with one inch blooms. You may get decent plants (or may not) from this generic potted, disposable roses. Unfortunately, since they aren't intended to be planted and grown on, the creators/suppliers usually give no information about them other than the trademarked series name and how to maintain them for the two weeks they are attractive under normal conditions.

Just because you buy a "Pink Kordana" makes no guaranty that it's going to be the same variety any two times you find it in a store or someone's garden. The product is "Pink Kordana", but if you look at the tag in the pot, you'll probably see a dozen or more code names which could be planted in that pot under that trade name. They resemble each other primarily in color range and propagation performance. Once given sufficient resources, it's anyone's guess what they'll turn in to.

If you want something which you can be given a more accurate, reasonable range of what to expect, it's going to require obtaining a mini which was selected and introduced as a specific name, where the same rose is always supplied when you purchase that name. Otherwise, you're just buying a "pink mini" and receiving any one of a dozen (or more) varieties. Kim