What are the origins of the surname 'Rymer'

Dear Rymercho, 

According to Kate Monk's Onomastikon (Dictionary of Names), Rymer is
an English name, which dates to the Norman era and denotes a
profession/tradesname.
Trade Surnames
<http://www.gaminggeeks.org/Resources/KateMonk/England-Surnames/Tradenames.htm> 

Rymer might be interconnected with "Rimmer", which could explain which
profession it describes.
RRImmer - New Zealand
<http://rrimmer.co.nz/> 

Graham Thomas establishes this in this research on names in Gloucestershire. 
"RYMER: Found in Chepstow and the vicinity and likely connected to a
family of clothiers called Rimer, who lived in Minchinhampton."
(SOURCE: Graham Thomas, "Gloucestershire Names and their Occurrence",
<http://www.grahamthomas.com/glocnames.html>).

It might be also from Suffolk: 
"First found in Suffolk where they were seated from early times and
their first records appeared on the early census rolls taken by the
early Kings of Britain to determine the rate of taxation of their
subjects."
(SOURCE: Rymer Coat of Arms,
<http://www.houseofnames.com/xq/asp.c/qx/rymer-coat-arms.htm>).

Further Resources
-----------------
Rymer Family Geneaology
<http://genforum.genealogy.com/rymer/> 

I hope this answers your question. Please contact me if you need any
clarification on this answer before you rate it. My search terms:
"Dictionary of Names" rymer, Onomastikon rymer, surnames rymer,
surnames , surnames origins, Rymer surnames origins, Rymer "origin of
the surname", Rymer "origin of the name", Rymer etymology

Thanks for that it was very intresting, funny that I am decendent of
the calculator. I wanted to make a gift for my grandfather for
christmas and I hope in this information I can find history relating
to our branch of Rymers from West Yorkshire.

I might change my name to Calculus Rymer!

Here is what the Brothers Grimm in their Dictionary of the German
Language had to say (based on the German spelling of the name):

"Verknüpfung auf diesen Artikel REIMER,  m., mhd. rīmęre, ahd. nicht
belegt, ags. rīmere, engl. rhymer, nebenform im älteren nhd. reumer
AVENTINUS 1, 560, 32 in M, vgl. reume neben reime, reumen neben
reimen. der ursprünglichen bedeutung von rīm zahl entsprechend
erscheint das ags. rīmere in dem sinne: a computer, reckoner,
calculator, mhd. rīmęre ist einer, der etwas in rīme bringt, der
dichter, ohne spöttischen nebensinn:..."

I am sure you understood that, but just to help:
masculine, middle high German:  rimere; old high German: no reference;
Anglosaxon; rimere; English; Rhymer, alternate form in older low high
German; Reumer  AVENTINUS ... (another source with related forms). 
With reference to the original meaning  of "rim" (number), the
Anglosaxon rimere seems to have the meaning:  a computer ..., one who
tallies up or makes things balance [accounting-wise], or one who
rhymes, without a negative connotation: ..."

http://germazope.uni-trier.de/Projects/WBB/woerterbuecher/dwb/wbgui?lemid=GR03660

That last bit is because the word did later assume a negative
connotation: a rhymer vs a poet.  The definition goes with a couple of
quotations, one from Goethe to the effect:  "You won't finder a rhymer
who doesn't think he is the best."

But I am sure the adaption of the word as a family name predates that,
so you are descended from a family of early computers and calculators,
predating Babbage's 18th c. Analytical Machine, Univac, et al.  ;-)
So don't swear at yours the next time it upsets you, it could be a
distant relative ...
(Sorry, I just had to add that; I didn't know your name would lead me to this.)
Myoarin

Thank you for the rating!