I have to name this:

[Co(H2NCH2CH2NH2)2]3+

And I think it is this:

bis(ethylenediamine)cobalt(III) ion

But can someone verify and check if I named it correctly. I am not sure if I am supposed to have the (III) or not.

I think it is named correctly. The III is needed to know that Co is +3 and not some other oxidation state. Of course, with the +3 charge, one would know that Co HAD to be +3.