The name of the Goddess is sometimes written as: Hecate and sometimes as Hekate. This can be confusing, but do not despair, both spellings are valid and refer to the same goddess!
The spelling of HEKATE (with a K) is closer to the transliteration of the name of this goddess directly from Greek into the English language.
The spelling of HECATE (with a C) is the Latin transliteration of the name of this goddess, as it was used by the Romans.
It is normal for Greek and other names in languages where a different alphabet is used (for example Russian) to be written in slightly different ways when transliterated into English, but Hekate is the more accurate transliteration, and therefore the one preferred by scholars writing about and also by devotees who honour the Greek Hekate. Those whose studies or devotion is focused more on the later form of the Goddess, as she was seen during the Roman period, may sometimes prefer Hecate – but this varies, many still prefer Hekate.
As an aside:
Heckate is never the correct spelling!
The Egyptian goddess Heket (Hequet) is not historically linked to the goddess Hekate. The “sounds-like” connection between their names is incidental, especially as we don’t actually know what Ancient Egyptian sounded like exactly, and as the “H” in Hekate in Greek is not pronounced in the same way. The goddesses also don’t share much symbolism or history in common, other than the general link to birth. Hekate has more similarities with Hathor (The Cow-Headed goddess) even though she was also not really historically linked to her, and of course with the Greco-Egyptian Isis (Egyptian Aset) with whom she was conflated, and also merged as Isis-Hekate in many locations throughout Europe and Anatolia (Turkey), as well as in Egypt.
Hekate is also not linked to the Egyptian God Heka. They both share a connection with magic in common, and of course another “sounds-like” but there is no known historical connection, or other similarities.