I would totally recommend you try to figure out if it's any known variety. The mint family has several species, and they hybridize very easily, so that makes hundreds of variations.
It might be a form of catmint. It would wise to look up the specific plant. They have different needs when caring for them. They do have an abundance of personality. As do all plants.
There are two ways that I know how to transplant mint. There is the standard method. Which is to dig out the root system, plant and all. Leaving a big enough dirt ball around the roots. Or you can splice a stalk off and start a new plant. Splicing os different for the type of plant. Both will shock the plant. The key is to not shock the plant too much. So dig carefully and make sure to water and give your plant some extra food and attention nefore during and after. Get a feel for how it's doing before hand. It will make the transplant a lot easier for the both of you.
Just a side note about mint that isn't magical or medicinal; if you keep it near or in your kitchen, it can help repel ants, due to the fact they abhor the smell of mint. I live in an area where ants are virtually impossible to avoid, but mint helps with this issue tremendously. (You never know how evil ants can be until they infest a freshly made birthday cake for one of your parents...)
In my own personal experience Mint, depending on how strong it may be, can be used to awaken senses connected and around your face. So can raddish shavings but thats a whole other ballpark. I usually love to use Mint and Lavender in a nice anti-congestant when say, if one where to have a slight cold or stuffy nose.
Blessed be!
Mint is also tasty in icecream, but with that I always thirsted for water ;)
Mint is awesome since it is very easy to grow once it's well rooted. sometimes it maybe invasive like oregano in which it may over take other herbs. I love it though i use it as soon as it grows :)
