Can I keep my current nationality, or do I have to give it up to become Irish?

From the Irish side, you can hold Irish citizenship alongside one or more other nationalities. Naturalisation does not ask you to surrender your original passport or citizenship.

The important caveat is your other country's law. Some countries do not allow their nationals to hold a second citizenship and may treat acquiring Irish citizenship as grounds to lose the original one. Always check the rules of your country of origin before you apply, because Ireland cannot control what another state decides.