Omniknight's Ultimate, Guardian Angel is refered to as Hammer Time, due to the fact that you cannot touch someone under it. And he has a hammer.
Nature's Prophet: His original name in DotA was Furion, but this was changed in the transition to DotA 2 due to copyright reasons. However, his actual name (prior to it being redacted) is very rarely used due to being unpopular and Furion is frequently used instead. Even some of the game files still refer to him as Furion.
Others know him as Nature's Profit due to his farming abilities.
Disruptor: "Dis Raptor," given his mount of choice.
Spirit Breaker: Space Cow, after the PyrionFlax guide to Spirit Breaker. This later became an Ascended Meme with the Three Spirits patch; Earth Spirit refers to him as a "space cow" in some of his responses.
Witch Doctor: "The Walking Fountain," because of his constant AoE heal and ultimate.
Dark Seer: "Dark Sonic" due to the spikes on his back giving him the appearance of a hedgehog, and his Surge ability allowing him to GO FAST.
Bloodseeker: "Pubseeker", due to his high popularity in public / pickup games. He also goes by the moniker "Bloodcyka" for his popularity among Russians in the low-skill brackets note the curse word "сука" is synonymous with foul-mouthed or uncooperative Russians in the fan community.
Windranger: "Windginger", because she's a redhead. note and because fans didn't like her name being changed from Windrunner
Venomancer: "Bananamancer", due to his old model's curved posture and bright yellow-green color.
Slark: "Fishi", due to his appearance and (as a ganker) inevitable comparison to Riki.
Hey, It's That Voice!: A lot of the voice actors worked on Valve's previous games, so it's not surprising to hear familiar voices.