How to install "PC Companion" software of Sony Xperia?

This program is specified for Windows only.

I searched but didn't find an alternate for Linux. So when a program simply does not exist for Linux, you cannot install it (at least with the native way).

You can use either Wine or VirtualBox and resolve your problem.

In case you just need to exchange files from pc to phone you can use ADB -> ADB and Sony xperia

From Ubuntu community wiki

• How to install and use Wine --> WineDB Sony Companion
• How to install and use VirtualBox--> Virtual Box and Sony Companion

Others have been using a virtual machine for this, sadly there isn't any support for Ubuntu on PC Companion (i just tried).

WINE support seems limited and running it on this end seems incredibly glitchy, but if it's only for the storage purpose then you can change the settings on your phone to USB Storage mode if you want to get into the contents on your device.