The name Rem in Hebrew letters is רם. 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.
רם
In short
Your name in Hebrew letters is רם. A Tanakh name: the name of an Arabian and an Israelite (first in Job 32:2; 7 mentions in the Tanakh). Meaning, per Strong’s dictionary (1890): “high”. Adding up the numbers of its letters gives 240 — the same as the Torah word ככר, “plain, talent, loaf”. That number points to Torah page 240 of 354 — in the portion Behaalotcha. What that portion is about: Lighting the lampstand; the second Passover; the cloud leads the camp; quail and complaints; Miriam and tzaraat. The verse that begins with the first letter of your name and ends with the last is Genesis 47:22. Each of these steps is laid out below with its sources. Every figure can be checked by hand.
You wrote “Rem” — this exact spelling is what was calculated: רם. 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 רם gives 240.
240
The number 240 is the Torah word ככר — «plain, talent, loaf» (Genesis 13:10).
And over the host of the tribe of the children of Issachar was Nethanel the son of Zuar.
This is from the portion Behaalotcha. What it is about: Lighting the lampstand; the second Passover; the cloud leads the camp; quail and complaints; Miriam and tzaraat.
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) — 800. A Torah word with the same number is קשת — “bow” (Genesis 9:13).
Reduced, each letter to one digit (mispar katan) — 6. A Torah word with the same number is בד — “alone, apart” (Genesis 2:18).
Ordinal: alef 1, bet 2 … tav 22 (mispar siduri) — 33. A Torah word with the same number is גל — “heap of stones” (Genesis 31:46).
Cumulative: a letter plus all letters before it (mispar kidmi) — 940. A Torah word with the same number is צמיתת — “permanence, perpetuity” (Leviticus 25:23).
Squares of the letter values (mispar perati) — 41600.
Building: the sum grows with each letter (mispar bone’eh) — 440. A Torah word with the same number is שמנים — “eighty” (Genesis 5:25).
The letters that come out are גי — not a word that stands in the Pentateuch. Atbash: letters mirrored, alef for tav, bet for shin, and the number of the resulting word — 13. A Torah word with the same number is אחד — “one” (Genesis 1:5).
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 240 appears in the classical books 35 times across 21 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 — 240. 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. רם has 2 letters: ר Resh, ם final Mem. The first letter is Resh, the last is final Mem.
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 רם appears in the Torah as a word 1 time. The first time is Deuteronomy 1:28. Another 5 times it stands with prefixes — “and”, “in”, “the”.
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 רם these are ר and מ. The Pentateuch has 7 such verses. The first of them is Genesis 47:22:
רק אדמת הכהנים לא קנה כי חק לכהנים מאת פרעה ואכלו את חקם אשר נתן להם פרעה על כן לא מכרו את אדמתם
This is from the portion Vayigash. What it is about: Judah pleads for Benjamin; Joseph reveals himself to his brothers; Jacob goes down to Egypt; the family settles in Goshen.
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.