@ZeroMile Its called linked FD feature, can also be termed as Sweep In-Sweep Out feature.
ICICI has it by the name of Money Multiplier, Kotak calls it Active Money, RBL Bank name it as Flexi FD / Linked FD, Yes Bank simply calls it Linked FD.
All are available online except RBL, for which you need to visit branch.
For further details you can check past messages posted by Vimal Garodia Sir and MVP Sir for better understanding