@kitten as a not really but kinda native, the first doesn't really sound that wrong? but the second one definitely is wrong, and the third is probably "prescritively" the most correct one
1) "Ich mag nicht den Schreibtisch" can be correct correct, but puts the stress on the "den". Could mean something like "I don't want this particular desk (but rather another one)"
2) is incorrect¹
3) is correct and the most common and just means "I don't like the desk"
¹ I mean grammar is made up and I don't particularly like perscriptivism but I digress