The name Shimei in Hebrew letters is שמעי. 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.
שמעי
In short
Your name in Hebrew letters is שמעי. A Tanakh name: the name of twenty Israelites (first in Exodus 6:17; 44 mentions in the Tanakh). Meaning, per Strong’s dictionary (1890): “famous”. Adding up the numbers of its letters gives 420 — the same as the Torah word ענש, “to fine, punish”. That number points to Torah page 66 of 354 — in the portion Vayeshev. What that portion is about: Joseph's dreams and his sale by his brothers; Judah and Tamar; Joseph in Potiphar's house and in prison; the dreams of the butler and the baker. The verse that begins with the first letter of your name and ends with the last is Exodus 12:15. Each of these steps is laid out below with its sources. Every figure can be checked by hand.
You wrote “Shimei” — this exact spelling is what was calculated: שמעי. 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 שמעי gives 420.
420
The number 420 is the Torah word ענש — «to fine, punish» (Exodus 21:22).
And the Midianites sold him into Egypt unto Potiphar, an officer of Pharaoh's, the captain of the guard.
This is from the portion Vayeshev. What it is about: Joseph's dreams and his sale by his brothers; Judah and Tamar; Joseph in Potiphar's house and in prison; the dreams of the butler and the baker.
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.
Final letters as 500–900 (mispar gadol) — 420. A Torah word with the same number is ענש — “to fine, punish” (Exodus 21:22).
Reduced, each letter to one digit (mispar katan) — 15. A Torah word with the same number is זוב — “to flow” (Exodus 3:8).
Ordinal: alef 1, bet 2 … tav 22 (mispar siduri) — 60. A Torah word with the same number is ילך — “he will go” (Genesis 3:14).
Cumulative: a letter plus all letters before it (mispar kidmi) — 1620.
Squares of the letter values (mispar perati) — 96600.
Building: the sum grows with each letter (mispar bone’eh) — 1470.
The letters that come out are ביזמ — not a word that stands in the Pentateuch. Atbash: letters mirrored, alef for tav, bet for shin, and the number of the resulting word — 59.
Filling: the names of the letters are counted — alef, bet, gimel… (milui) — 590. A Torah word with the same number is שרץ — “swarming creatures” (Genesis 1:20).
The number 420 appears in the classical books 5 times across 4 works. The earliest mention is בעל הטורים על התורה (~1300).
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 — 420. 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. שמעי has 4 letters: ש Shin, מ Mem, ע Ayin, י Yod. The first letter is Shin, 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 שמעי does not stand as a separate word in the Torah, but appears 3 times with prefixes — first in Êxodo 6:17.
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 שמעי these are ש and י. The Pentateuch has 2 such verses. The first of them is Exodus 12:15:
שבעת ימים מצות תאכלו אך ביום הראשון תשביתו שאר מבתיכם כי כל אכל חמץ ונכרתה הנפש ההוא מישראל מיום הראשן עד יום השבעי
This is from the portion Bo. What it is about: Locusts, darkness and the death of the firstborn; the Passover lamb; the exodus from Egypt; the commandment of tefillin.
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.