Cats’ Strand (Ruthwell), Catstrand (Dumfries) and Cat Strand (Kells) all look to be transparently formed from CAT and STRAND ‘a little stream or run of water, a rivulet’. This is how the Place-Names of the Galloway Glens interprets Cat Strand (Kells)  and is behind the rather more elaborate explanation the Ordnance Survey Name Book gives for Catstrand (Dumfries):
“This name applies to where a small stream crossed the road at the top end of [the] Kirkgate. The name [originates] from the fact of the place [having been] formerly haunted by witches [in] the shape of cats.” 
Another possibility is offered by John Mactaggart’s Scottish Gallovidian Encyclopedia. He defines CATSTRAN’ as ‘a very small stream’.  This is the DSL‘s only citation for this word and, other than these places-names, I’ve not seen it anywhere else. 
It’s hard to know if the names above are CAT + STRAND or CATSTRAN’. CAT appears in plenty of local place-names, including Cat Syke (Gretna, Westerkirk) which is the eastern D&G equivalent of Cat Strand. And there are several ‘animal’ + STRAND place-names in Galloway: Otter Strand (Minnigaff), Goat Strand (Carsephairn, Girthon, Borgue), Hare Strand (Carsephairn), Heron Strand (Carsephairn), Ged Strand (Balmaclellan). The size of the stream might offer a way in, but with only 3 examples so far, there’s not much to go on. Perhaps more will come to light in estate maps and field-name surveys.
Update 18/08/2021: I spotted another CATSTRAN’ while reading ‘The Gold Wells of Cairnsmore’ in Lowran Castle by Robert Trotter. It’s used in Mactaggart’s sense of ‘a very small stream’. It also antedates the Mactaggart example by two years. No a muckle antedating – but it’s ma first yin an A’m fair pleased wi it!
Here’s the extract where it appears:
“From its [Cairnsmore] summit also, rushes many a torrent stream, wherein the hunter’s moon casts her clear light, as the fleet roe of the wood drinks the golden water from the sparkling stream. There Dr Dodds placed his water mills, anointed with an oil, the name of which was never yet known to the most cunning artisan, ‘north of the Tweed.’ They, in form and size, resembled those made of rushes by the school-boy, and placed in the cat-stran’ by the village school; and so powerfully attractive was this oil, that every morning before the sun rose above the horizon, he carried them home, their spokes thickly plated with the pure gold from the dashing stream.”
You can read Robert de Bruce Trotter’s account of the ‘The Goold Mills’, from Galloway Gossip, here.
Plenty of places take their name from a visual resemblance to something else. Boat Rock, Whithorn is “shaped nearly like a boat” and Maidenpap, Kirkgunzeon “derives its name from its protuberant shape somewhat resembling a female breast.” There’s a sweet spot, somewhere between rock and hill, where the outlines of these names stand out clearly on the map. I’ve found 37 so far, with ‘fiddle’ being the most common shape. [I’ve taken ‘square’ to be a noun like ‘diamond’ rather than an adjective like ’round’ or ‘long’.] Here are the numbers so far:
“A small plantation on the lands of Golielea, its wood consists chiefly of oak. It had formerly been the form of a cocked hat hence the name.” OS1/20/70/3
“A small plantation on the lands of Goldielea consisting of oak trees this plantation has been planted on the site of a former one – which had been planted by Colonel Maxwell – its shape was that of the figure of a cocked hat hence the name.” OS1/20/70/52
This name appears on the most recent OS map. It appears to be fairly recent as it isn’t marked on any of the maps hosted on the NLS website. The ‘dragon’s eye’ is a small pool with an island (presumably the dragon’s pupil) in the middle.
“A wood of spruce fir of about 30 years growth. It is situate on the Eastern slope of Bl[aze] Hill and was so called from its being shaped somewhat like [a] fiddle. Not known, consequently expunged being so insignificant.” OS1/10/50/160OS1/10/50/160
This plantation is marked on the 1st ed. six-inch OS but is unnamed. Both this and Horseshoe Plantation, Kirkconnel (below) are shaped – to my eye – like horse hooves rather than shoes. Horseshoe Plantation, Caddonfoot SLK (NT 439 332) is laid out in classic horseshoe shape.
“This name applies to a triangular piece of land held as a small farm or croft by William Corkran, The property of Colonel McDowall of Logan. Lies midway between Clash Hill and Muldaddie Hill.” OS1/35/82/3
I assume the reference here is to JIB ‘a triangular sail’. However, it’s worth noting that Scots JIB is ‘a protective leather covering for a stone-mason’s left thumb, used to prevent chafing by the chisel [from its triangular shape, like a jib-sail.]’ JIB in DSL
27/06/21: Carole Hough (2001: pp. 42-43) has written about the field-name The Jib in Linlithgow, which Macdonald’s (1941, p. 153) The Place-Names of West Lothian interpreted as a shape-name. Hough notes that shape-names don’t often refer to sailing and that The Jib could instead be grouped with place-names referring to sites of executions, drawing comparisons with English names such as Gib Close and Gibbet Cospe inter alia. This should be borne in mind here as a possibility.
Against this interpretation are the fact that both Jib and The Jib refer to triangular pieces of ground and that and that overwhelmingly Gallows- is used in Galloway (and elsewhere in Scotland) in place-names associated with hangings; I believe Gibbet Hill, Crossmichael KCB is the only gibbet place-name in Galloway. And as the Place-Names of the Galloway Glens notes, Scots gibbet can refer to devices for hanging pots and pans not just the gibbet: “there may have been some gibbet associated with this hill which was not actually a gallows.”
So, while it’s possible that Jib might refer to a place of execution, I think it’s more likely that the name refers to its triangular shape and that this name adds weight to the argument that The Jib in Lithlithgow is a shape-name after all.
“A small patch of arable land at the south end of Ever Holm. It is bounded on the north and west by a row of forest trees, and on the south & east by a wall that forms part of the southern boundary of Ever Holm. It owes its name to its shape; being shaped like the quarter of a cake.” OS1/10/2/11