sifus, as carry the cash no longer safe nowaday , mind to share what is the better option to move funds from one bank to another bank for FD deposit?

There are an amount limit for online fund transfers to other bank (but not sure to do it over the counter). Then how about banker cheque? will the bank accept it if I carry the banker cheque and ask for new FD account opening? Then what should I put as payee name? (My own name or the bank name?)