There is no completely satisfactory explanation of Lingoed. The "obvious" derivation from Welsh llyn, 1ake, and coed, wood, is unlikely, given that, as Bradney points out, there is no sign of a lake hereabouts. (Morgan, though, suggests that llyn may simply mean 'pool', rather than 'lake', which is slightly more plausible since there is a small pool near the church.) Osborne and Hobbs offer the suggestion that llyn is an abbreviation of celyn, in which case celynnig and (ce)llyn(n)goed mean the same thing, i.e. holly wood, but there is no evidence that the name changed over time in this way. In fact, both forms are often found together in documents from around the same period (for example, both Llangattock Clennyg and Llangattock Llyngoyed are found in Quarter Session documents of 1576-77).
The first date at which the name appears in the current form is 1348, when it is given as Lancadok Lyncoyd. Significantly, other documents from around this time clearly indicate that two different places are meant: Lancadok et Lyncoyd Capella in 1348 and 1349, Llancaddock by [iuxta] Llincoed in 1397 and Llan Cattoge Iuxta Lyncoyd in 1434. The first two of these documents refer to "Lancadok et Lyncoyd Capella, Killitha"; Killitha is almost certainly a form of modern Celliau, which indicates the other area, in the north-east of the parish, that was used in the alternative name for the parish.
Osborne and Hobbs believe the name derives from the adjacent Grange of Llyncoed. This is plausible, but does not explain how the grange itself came to be so called. In fact, it is not the earliest known use of the name: a letter from Pope Eugene III to Prior William of the church of St John in Llanthony in 1146 confirms the Priory's various properties, including land "next to Linchoit" and other land "near St Michael" [Llanfihangel Crucorney], which allowed them "use of the forest of Linchoit". (These privileges were first granted by Innocent II in 1131.) The Grange of Llyncoed was granted to Dore abbey by Henry II and confirmed by Hubert de Burgh in 1228-29. In a document relating to the Lay Subsidy of 1292 there is reference to "land of the lord abbot of Dore at [or near] Lyncoyht". The Reeves returns to the lord of the manor in 1257 refer to the trunks and the dead wood sold in the park of Lyncoyt. This and later references clearly indicate that this was the name originally given to the lord of Abergavennys hunting area, later known as Park Lingoed or simply the Park. The park is equally likely as the source of the second, identifying element in the name, but again offers no clue to its meaning.
Hubert de Burgh's confirmation of the grant enumerates its bounds, which enclosed 443 acres of tithe-free land: "the land of Lincott on the stream Troyn [Troddi?]", with these bounds, "from the land <of> <L>agoking to the head of Troyn Brook, from the head of the Troyn to the lands of William de Braos (as the brook runs down), from another part of Laggoking’s land to the Mora [Monnow?] which is below, from the mora to the land of Seysil son of W<mni>, from there to the road from Grosmunt Villa [Grosmont] to St Michael’s Villa [Llanfihangel Crucorney], from the road to the said land of William de Braos as the said land is separate from my land of Grosmunt." Apart from William de Braos, lord of Abergavenny, the persons named can't be identified. The Troddi was the eastern boundary of the lordship of Abergavenny and the grange ran north from here to the ancient L1anfihangel - Grosmont ridge road over Campston Hill, then westwards until it again turned south and met up with the lord Abergavenny's park Lyngoed.
Around the year 1540 John Leland journeyed from Hereford to Abergavenny via "Lincote wode" (the mileages given would place it on Campston Hill, which is where the grange was located). A little later, in 1602, George Owen's Description of Wales was published, in which he lists "Grismond" (i.e. Grosmont) as one of the "forestes and greate wooddes" of Monmouthshire. Henry Owen, his late nineteenth century editor, claims that Llingoed was the Welsh name for this "great woodland of olden times", but unfortunately he offers no evidence for the claim. It's worth noting, though, that de Burgh's grant refers to "Grosmont Forest" as a separate area, so at best Owen was only half right. However, the park, the grange and the Llanthony Priory properties and privileges together cover a wide area and give strong support to the idea that Llingoed was the name of an extensive forest extending from the Skirrid towards Grosmont and probably stretching down to the river Monnow.
That Lingoed derives from the name for this area of woodland makes a lot of sense. There is a Welsh word 'llingoed', a collective noun for tall, straight trees and also for fine-grained wood. Rather than a lake, then, or holly trees, this woodland seems to have been named after the nature of its trees and the quality of the wood they provided.
The map below, reproduced from Rees, shows his reconstruction of the area. His location of Lyngoed is slightly out: the park is further west, on the other side of the stream (now known as Full Brook) and from there Lyngoed stretches north and east into the adjoining lordship and parish of Grosmont, where Lincoyt is indicated.
Sir Joseph Bradney, A History
of Monmouthshire, Volume 1, Part 2.
Richard Morgan, Place Names of Gwent
Graham Osborne and Graham Hobbs, The Place-Names of Eastern Gwent
George Owen, The Description of Pembrokeshire, Volume 3 (ed. Henry Owen, 1906)
William Rees, South Wales and the Border in the Fourteenth Century