Meaning of Tazmeen and if it is Islamic

You can use Tazmeen for a name, though it is not used by Arabs as a name. It means to arrange, align, put in order, or include. It also means "long period of time". This second meaning ("long time") is a Quranic name since it comes from the Quranic root Z-M-N. The first meaning is not a Quranic name.

Here are more details about the name if you are interested:
In Arabic Tazmeen could be two words. One of them is with the Arabic letter zaad and means to "put things in order", to arrange, align, classify, or to include, embody, embed. Another is with the Arabic letter zaal, and this one means to find out the date of something, it also means "long period of time".

Many websites mention other supposed meanings for this name, but this is all there is to it in Arabic. Many websites put the Arabic spelling with the letter "zaa" for the "z", as in:
تظمين

There is no such word in Arabic or anything like it. This is just a common misspelling of Tazmeen with the letter "zaad":
تضمين
Which as said above means to arrange, align, organize, or include.