Time Machine won't recognize external hard drive

I bought a new 2 TB hard drive. I tried to partition it to use part for Time Machine backup and part for normal storage. Time Machine won't recognize the disk, although it is on my desktop and I can copy files to and from it. Disk Utility shows it has only 500 GG. I tried re-formating the disk from Disk Utility, and it seems to reformat OK, but still shows only 500 GB and Time Machine doesn't see it. I am using APFS format. I tried Disk First Aid, and it says everything is OK.

How can I fix this 2 TB external hard drive so Time Machine will use it? Is it possible to use half of it for Time Machine and half for normal use?