Catalina automatically formats your drive using APFS. APFS creates five "synthetic" or logical volumes all of which share the space of the single physical drive. APFS allows several volumes to share the same space which eliminates the need for creating separate partitions for each volume. The five volumes are set up in one "Container." They are:
- Macintosh HD
- Macintosh HD - Data
- Preboot
- VM
- Recovery
Of these five, only one is visible on the Desktop - Macintosh HD. This volume contains a read-only copy of macOS system files. Applications and user accounts are stored on Macintosh HD - Data. Macintosh HD contains special links, called "firm links," to the files on the Data volume. Thus, the user will find that Macintosh HD looks to the user like a normal, single device. The other volumes are invisible.
Now, if your other computer has two volumes named Macintosh HD - Data, then the drive was not erased correctly before installing Catalina. One of those Data volumes is from the previous system installation, probably, Mojave. You can use Disk Utility to remove one of them but it's really hard to know which one. You will need to examine them carefully. Alternatively, you can simply erase everything from that drive, install Catalina from scratch, restore your data from a backup.