For such a simple surname there are many links and the Farr Dna project seems to prove this
My own branch through family myth goes back to scotland from there im unsure whether there are pictish gypsy or celtic clan roots going to use the dna to see.

By far the most populist branch seems to be the the hertfordhire east england branch. I dont think im linked to this lot (will have to see) but some of my own branch emmigrated across the world.


Below are some origins i have heard for the Farr Surname over modern available history admitted some are very sketchy and will not apply to the majority.

Farr crest- Scottish cross on it.

Farr/le fere - Anglo saxon Norman /hugenort - Bull, Bullish
Fawr/Far - Galic - great applied to island mountains etc
Farr - Sea opening passage / part of boat
Farr - Norwegian Shepard
Faa - Scotish gypsy romany north india
Farr horsemen of plains eastern baltic steps
And obviously modern day far used as a distance far away.

Farr signifcant places
Hertfrodshire -streets
Herefordshire welsh borders
Cornish
Ireland lochs villages streets
Scotland Farr parish sutherland, Farr Inverness , Farr near loch lomond? Farr stone.
France and scotland have shared history.

Names
Earls of Farr links to clan Mackay, Ross Mcdonald and the isles. Black angus of Farr
Gypsy johniee faa king of little egypt.
Other links with broken clans Macfarland? Gordon? Macphearson.


Myths claimed long histories ive heard
Irish / scottish pictish
picts ancient americans crossing form scandanavia (very sketchy ;))
French Huguenot protestants
Germanic
steppes
Gypsy
Mongols / iranians
Ancient farr herdsmen traveller form east.


My own opinion all R dna which is shared by most of the UK and most Farrs apparantly according to the genetists over many thousand years has eastern orgins.
The name may have followed this path in waves of immigrants over millenium before this as people move this way, being adopted and changing with the people.