when transferring information from old iPhone to new iPhone will voicemails get transferred too

Yes, if you do it the right way: iPhone: Transferring information from your current iPhone to a new iPhone

You may get one or more responses from spammers trying to sell you 3rd party software to do this. Please ignore them; maybe they will go away.

Voicemail are kept by and are a function of the carrier. They are not stored on your phone. So when you get a new iPhone, as long as you are using the same phone number, you will be able to access any saved voicemails.