I am Abdul Athif. Athif means "kind". So I was given as Abdul Athif meaning "Servant of the kind" or "slave of the kind". But I don't find the name Athif in the 99 names of Allah. Is it going against Thawheed? Should I change my name to Athif alone?
اللطيف (Al-Latif, sometimes transcribed as Al-Lathif) is one of the 99 names of Allah, meaning the Subtle, or the Most Kind. Abdullathif (عبد اللطيف) would be a perfectly valid name for a Muslim.
I do wonder if your name is just a variation of that (transliterations can make that really hard to tell sometimes), with the double-"L" of Abdullathif simplified into a single-"L" (Abdulathif, wherein the "L" gets retained on the Abdul rather than the Lathif when both parts of the name are written separately)
If that's the case, I don't see any problem with keeping the name, although correcting the spelling so it's more clear that it does still refer to one of the Names of Allah would be prudent.
If, however, your name is derived from the Arabic عاطف (Atif/Athif, "Kind"), another common Arabic name which is not one of the Names of Allah, then yes, retaining the "Abdul" would be problematic, as it involves you identifying as the slave/servant of something that is not Allah.