The name Hegai in Hebrew letters is הגי. Below: how its number adds up, which page of the Torah it falls on and what verse stands there. Everything is computed, nothing is guessed.
הגי
In short
Your name in Hebrew letters is הגי. A Tanakh name: a eunuch of Xerxes (first in Esther 2:3; 4 mentions in the Tanakh). Adding up the numbers of its letters gives 18 — the same as the Torah word חי, “living”. That number points to Torah page 18 of 354 — in the portion Lech Lecha. What that portion is about: “Go forth”: Abraham leaves Haran; the promise of land and offspring; the covenant between the pieces; circumcision. The verse that begins with the first letter of your name and ends with the last is Genesis 4:14. Each of these steps is laid out below with its sources. Every figure can be checked by hand.
You wrote “Hegai” — this exact spelling is what was calculated: הגי. A name from the Tanakh — its Tanakh spelling is used. If your name is spelled differently, correct the Hebrew spelling and the report is recomputed.
Adding up the letters of the name הגי gives 18.
18
The number 18 is the Torah word חי — «living» (Genesis 1:20).
And there was a famine in the land; and Abram went down into Egypt to sojourn there; for the famine was sore in the land.
This is from the portion Lech Lecha. What it is about: “Go forth”: Abraham leaves Haran; the promise of land and offspring; the covenant between the pieces; circumcision.
Other ways of counting
The tradition counts the same name in several ways. The main one is above: each letter is its number. The other eight are old and checkable too; each gives its own number, and many of them have a Torah word with the same number.
with finals and ordinal — 18. A Torah word with the same number is חי — “living” (Genesis 1:20).
Reduced, each letter to one digit (mispar katan) — 9. A Torah word with the same number is בוא — “to come, enter” (Genesis 2:19).
Cumulative: a letter plus all letters before it (mispar kidmi) — 76. A Torah word with the same number is עבד — “servant” (Genesis 9:25).
Squares of the letter values (mispar perati) — 134. A Torah word with the same number is פדן — “Paddan-aram” (Genesis 25:20).
Building: the sum grows with each letter (mispar bone’eh) — 31. A Torah word with the same number is אל — “to, toward” (Genesis 1:9).
The letters that come out are צרמ — not a word that stands in the Pentateuch. Atbash: letters mirrored, alef for tav, bet for shin, and the number of the resulting word — 330. A Torah word with the same number is צמר — “wool” (Leviticus 13:47).
Filling: the names of the letters are counted — alef, bet, gimel… (milui) — 109. A Torah word with the same number is צידה — “provisions, game” (Genesis 27:3).
The number 18 appears in the classical books 36 times across 24 works. The earliest mention is ספר קרניים (~1400).
Every letter of the name explained, the words and namesakes with references, the Hebrew date, the letter and tribe of the month, day 861 of your life (±1), the psalm by age, the attestations from the classical books — a PDF sent to your email.
The number of the day, every morning
Every date has a number too. Once a year it will match the number of your name — 18. The channel posts one number a day, one verse and the Torah page it lands on. Nothing after it, no mailing list.
Hebrew is written from right to left. הגי has 3 letters: ה He, ג Gimel, י Yod. The first letter is He, the last is Yod.
For an engraving, a sign or a tattoo, show the spelling to someone who reads Hebrew: transliterating a name is a choice, not the only option.
The name הגי does not stand as a word in the Pentateuch — as with most names, including many Tanakh names from the later books.
The verse of your name
There is a custom: at the end of the prayer one says a Torah verse that begins with the first letter of one's name and ends with its last. For הגי these are ה and י. The Pentateuch has 12 such verses. The first of them is Genesis 4:14:
הן גרשת אתי היום מעל פני האדמה ומפניך אסתר והייתי נע ונד בארץ והיה כל מצאי יהרגני
This is from the portion Bereshit. What it is about: Creation in six days and the Sabbath; Adam and Eve in the garden; Cain and Abel; ten generations to Noah.
Each Hebrew letter has a number; a word's number is their sum (alef 1 … tav 400). The page is the remainder modulo 354: the Torah divided into 354 pages of 861 letters, as the lunar year has 354 days. Everything can be checked by hand.