Hi & welcome, Vito!
It's looking like a Bromeliad to me too. Adding a pic looking down at the top of the plant might help someone recognize it. It's not necessary to know exactly which one it is to answer your question about the babies/pups though. If/when they have their own roots, they can easily be separated. Yours Separating is not necessary but definitely possible for your plant, depending on your preference.
If your plant is in a pot without a hole in the bottom, that can be tricky because adding too much water 1 time could make your plant ill or even be fatal. A toxic buildup of tap water substances like lime & fluoride, as well as residues from fertilizers, can also occur and make some plants ill.
Pretty pots without a hole are often used as cache/catch pots to hold/disguise a less decorative but more functional pot. When it's time to water, the inner pot can taken out, the plant can be watered at a sink, shower, or outside so the excess water can drip away freely, then put back into the decorative pot when it's finished dripping. This allows the best of both - avoiding a buildup of substances, no risk of too much water causing roots to rot, and a pretty pot to look at.
