Naturalisation | Country of birth | Czechoslovakia or Czech Republic

Hi.

I am applying for naturalisation and I am not sure what to put in the "Country of birth", I am Czech, but the country was called Czechoslovakia when I was born later Czechoslovakia split to Slovakia and Czech republic.

Also does that mean that I had more than one nationality? The same applies to my parents - they were born in Czechoslovakia but their nationality is Czech.

Thanks for any advice.

Input as your passport/official documents state.