I received my bonsai as a gift for my birthday and have been doing my best to take care of it. I feel it would be beneficial for me to know the name of the exact species I own. Thank you in advance.

everyone else is correct, bring it outside asap. i'm not sure where you are in arizona, but you are probably close to zone 7. your tree is most likely a japanese juniper, these really prefer to be in a colder zone, but as long as you pay close attention you can make it work. you will want to check the soil several times a day. gently dig down an inch or so and if it's still moist then let it be. if it is dry, give it a good soak. as you are watering it don't worry about getting it too wet, the soil and pot are designed to not hold too much water. misting it once or twice a day is not a bad idea either. here is a good reference for general care: http://www.bonsai-bci.com/species/garden-juniper.html

Hi, sorry it took so long to get back, but unfortunately I don't think it would have mattered much. Ligustrum is just plain privet, the hedge that lives around everyone's lawn and most definitely an outdoor only, 365 plant. It would have needed to be outside (if with some protection in winter depending on where you live and the pot size) to have gradually adjusted to the cold in autumn and then the opposite in spring. It needed full sun all day pretty much except maybe in the SW, where it's unlikely to have been sold or grown anyhow. What it didn't need was water twice a DAY (no HOUSEplant needs that or anything close to it), and the sunniest window (all day) that you have if it were to even have a hope of living inside. Except for tropical and a few semitropical trees, everything else needs to be outside all year to experience the cold dormancy needed to renew it for spring. Please don't spend more on trees or plants til you research more about the species... do both of you (and your wallet) a favor :).

It is (was) a juniper. Unfortunately it is gone now. For future reference it needs to be outdoors all the time. It needs that winter dormancy but being in a pot it also needs some protection like an unheated garage/shed. During spring to fall it should be out in the sun. They like to be on the dry side.