There is one thing you have to know before, and is that if the parameters for text styles or dimstyles that will be renamed with a name of an existing one, are different, they can NOT be associated with that style, so you will have to decide which will be the new name., for example if the name of original one is MYSTYLE, the new similar but not equal could be named as MYSTYLE1, MYSTYLE2 ecc if you are bonding different dwg
The application you have shown was taken from CADTUTOR , and I understand somebody gave you the same answear