I think I’ve got a fairly good grasp on how plant names work. Under the Linnaean system, you give them a genus and a species, such as Alchemilla mollis. Most often there is more than one species, such as Alchemilla vulgaris, which is a smaller relative of the mollis. As with most things though, the closer you look, the more complex it gets, with varieties, subspecies, hybrids and more (see this Gardeners’ World article for a broader introduction).
I’m a bit confused about this rose, seen at RHS Rosemoor yesterday, which was actually labelled Rosa Tynwald ‘Mattwyt’. Rose breeding is a whole discipline in itself. The best I can work out is that it as hybrid tea rose with the cultivar name ‘Tynwalt’ but exhibited as ‘Mattwyt’ (see this specialist site).
Whatever the name (I’m desperately skating round the Shakespearian cliché), it certainly smelled sweet and looked lovely.