Short answer: No. Your question doesn't say what filesystem is on the disk you're moving, but the fact that it contains a UID on a Linux system suggest it's some variant of EXT, and the UID, GID etc are stored in the INODE structure as integers - see https://ext4.wiki.kernel.org/index.php/Ext4_Disk_Layout#Inode_Table.
If you want to move data owner-agnostically then you could format your disk to something like FAT32 which doesn't store ownership information, but then you lose things like case-sensitivity in filenames and journaling to protect against write errors.
If you only have a small number of computers then your best bet is probably to create all your users and groups with the same IDs. Read through the useradd/adduser and groupadd/addgroup documentation for your particular distro to see how to specify the number.