My  maiden name is Jacqueline Grim, and I started researching our family history about 20 years ago with my father, He was always telling me lots of stories about growing up in the East End in the 1920's. He said it wasn't a big family, and only knew one sister and niece and nephew, so not much to go on. I subsequently discovered quite a few cousins my dad had never met.
Sadly when my paternal grandmother died my grandfather burnt all the family photos, but as my Dad was a keen photographer I do have some recent  ones to treasure. We spent many hours at St Catherine's House ploughing through all those heavy old ledgers, and had lots of papers with names and dates; proving that the name of Grim was not so limited.
Dad passed away in 2008, but I continued the research, blessed by the internet

i visited the Roots Tech Exhibition when it came to London in 2019 and signed up with the Guild.

The name of Grim is not very wide spread in the UK  now; the Oxford Reference Book of Family Names identified  55 people of this name on the 1881 census, and currently in the UK 61 and 1 in Ireland.

I am looking specifically at the name GRIM; I know there are lots of variants Grimm, Grime. Grimes  etc but I was daunted by size of  spread.  I found many references to GRIM so that  where I am concentrating at present. My 2XG grandfather had 6 children so that builds a big tree.

I have been studying an on-line degree in Genealogy Studies which has involved quite a lotof my time with assessments and stories of my immediate ancestors which I hope to publish soon.

I am currently looking into the history of the village of Grim/Grymsthorpe in Lincolnshire. As part of the Danelaw area there are some old family groups in the 17th and 18th centuries, but not many names bnow.

There are some theories on the origin.

A search on https://forebears.io/ has given a great deal of information. There is an amazing global spread of the name over  75 countries in the world.!!!  The name has origins in Old English, old Norse and Germany, it is also found as a forename in some countries. 

Definitions of the name; Scandanavian    the word means face or mask. Grim was the nickname of Odin when he went on his travels in disguise
                                            Old English       This could define a person's character or visage
                                             Old High German  spelt with 'mm'

Searches made on the Domesday book of 1068 and 1088 show approx 27 men by the name of Grim in England. They appear most frequently in Lincolnshire, Lancashire, Nottinghamshire, Cambridge Suffolk , Essex and Yorkshire, part of the old Danelaw, there was also a small cluster in Warwickshire(part of the old kingdom of Mercia) 
There are also many with with grim in a compound; Wulfgrim, Grimkil, Thorgrim,  Grimbald etc

Looking through the history of Cambridge University I came across mention of  two cousins who were tutors in Oxford who came to Cambridge to set up their own school of learning.

Another name to conjure with is that of Edward Grim, a monk who was with Thomas a'Beckett in Canterbury Cathedral at the time of the assassination. He 
wrote an account of the event, and I believe was wounded by one of the knights. He may have been a Norman monk. We know historically some Vikings settled in Northern France,( Normandy)

No other names spring to mind, so it appears that Grim men settled down to uneventful lives

There were some family groups in Scotland that I have yet to cover, and I believe that there were many families in Ireland (British and Irish Roots  website).

There are some places that have the name; Grimsby  -by  a term for a settlement, again of Norse origin. and Grimsthorpe in Lincolnshire. -thorpe  is a Norse reference to a  farm or settlement hence possibly Grim's farm. However many Viking settlements were based on earlier Saxon sites and names became mixed as nations intermarried. The current frequency of the name based on 1921 census shows 75 people in England and Wales scattered over a wide area

No figures to quote, as I mentioned earlier the name comes up in about 75 countries . spreading east from the Scandanavian  countries, across Europe, the near East, My initial start with the occurrence in English  Counties: Using parish registers on line I  have worked from 1500 -1900. In the 16th century the name  is found in 12 counties; in the south of England, Cornwall, Devon Somerset, up to Gloucestershire and Hertfordshire. across to Essex. to Lincolnshire, Lancashire, Warwickshire and Bedfordshire as single family units, 
In 1500/1600's there are 2 large groups of families in Yorkshire and Leicestershire with smaller groups in Lincolnshire and Essex.

By the 1700s there has been some population change. The main clusters are now Leicestershire, Lincolnshire, and Northamptonshire in the east of England and  new settlements in Warwickshire and Lancashire, on the west of England. we can a see a sharp decline in Yorkshire.
There are  also incomers from Russia, Holland, Germany, Hungary and France

1800s In the early part of this century the main centre are Northants and Warwickshire

1841 Census  102 people in England. 1/3 to be found in Middlesex; 

By 1911 Census the population in England is recorded as  50, 28 living in the Middlesex area

SCOTLAND

Scotland's People website has some parish records back to mid 1500s. There are 3 main clusters of settlement based on the east coast;  Brechin, Montrose and Monifieth
I was able to check birth registers for these parishes;
1500/1600s  35 births
1700s 29 births
1800s 9 births

Overall the main group was in Brechin

1841 Census   17 people mainly in 3 family groups
1861 Census 14 people mainly in 4 family groups
1911 Census 2 single people

WALES

I have not found any families with the name of Grim, apart from my brother in Pembrokeshire 

IRELAND The name was common in Ireland, presumably mainly from Scandinavian settlers in the first century. This was a rural country. More research to come here. 

USA  The name is found quite widely in the United States. As this is comparatively a newly settled country. I am investigating the available census returns

I did a personal DNA test with Living DNA, which was very interesting

The results show a 100% British ancestry on a recent basis

Devon                          24.2%
North Wales               16.8%
SE and S England        17.0%
Ireland                          8.5%
Northumbria               8.4%
Yorkshire                      8.6%
Cornwall                       4.5%
Aberdeen                     3.1%
NW England                 2.4%
East Anglia                    2.2%
S Central England        2.0%
N Ireland &SW Scot    1.1%

On the distribution map there is a gap across the middle of England south of the Humber across to Cheshire. It picks up again south of the wash across to the Severn,

The analysis from Ancestry DNA is much more vague, it completely omits the northern half of England, but does say possible ancestors from North West Europe.(Scandinvia, Low countries?)
They identified  314 possible 4/6^th cousins
Living DNA identified 331 4/6^th cousins