Tamjida (or Tamjidah and Tamjeedah) means "act of glorification", "act of exaltation", when someone is glorified, exalted or praised.
It can be used by Muslims since the meaning is good. It can only be used for girls since it is a feminine name, the male version is Tamjeed/Tamjid.
It is not directly mentioned in the Quran, but it is derived from the M-J-D root which is used in the Quran and is the source of two of the 99 names of Allah: Al-Majed and Al-Majeed. For this reason Tamjid and Tamjidah are indirect Quranic names.
Tamjidah is pronounced as TUMble + Juice + nEED + hUmble