we have our own CRM where we enter the counterparties, they have phone numbers and a name. Can we substitute this name in the panel "extensions" when making a call if it is in the database? CRM uses mysql
You should do this in the Asterisk dialplan. If you use FreePBX or Issabel, you have the Superfecta module that can check numbers over a variety of sources, including your own Mysql queries, and set the callerid name variable to the call.. FOP2 will display name/number by default with no special configs, so there is nothing to do in the FOP2 side.