@Chowdhury, Nasim (HC/SC) Welcome to Microsoft Q&A thanks for posting your question.
Server Name Retention: The Flexible Server will retain the same name as the Single Server after the in-place upgrade. This ensures a seamless transition and minimizes the need for changes in your applications or services that rely on the server's name.
Connection String: The connection string for your databases should remain the same post-migration.
VNet and Subnet Selection: there is no option to select the target Virtual Network (VNet) and Subnet for the newly created Flexible Server.
Regards
Geetha