First the bitness must be correct with lazarus. In 32bit Lazarus you can only use 32bit dll. 64Bit Lazarus need a 64 bit dll.
Second you have to place the second dll in the same folder like your executable is, this version must have the bitness of your app !!!
Rename works, if the version and bitness is ok. Attention, often it is not clear what bittness you have in the dll, because the naming have no schema.
BTW: For the App you are able to change the path of the dll (and so for linux as well) by code. It is possible for zeos and SQLdb, but implemented in a differnet way.