Jehovah is the name of God in the Abrahamic religions (originally just Judaism, but later Christianity and then Islam, plus a variety of other smaller offshoots). The name is written as "יהוה‎" in the original Hebrew, and translated from Hebrew to English as "YHWH" or "Yahweh." "Jehovah" is what you get when the name takes a linguistic detour through Latin—much like "ישוע" ("Yeshua") is "Joshua" when translated directly to English, but becomes "Jesus" when it passes through Latin.

The name of the Jehovah's Witnesses refers to "witnessing" in the sense that you'd call a witness to testify in court, in that they're prepared to present the story of their personal experience as a reason for others to be convinced.