No, except yes
TL;DR: ‘Wormtongue’ is a deliberately negative name given by his enemies, so it can’t be faulted for being pejorative, even if it’s not as unflattering as it might seem to modern ears. But ‘Gríma’ itself isn’t much better!
As Mary points out, ‘Wormtongue’ is a nickname applied to Gríma by his opponents (which, Gandalf implies, is everyone but Théoden). We’re not told exactly how Gríma—a sly schemer in a kingdom where warlike deeds are prized—came to be so influential, but it certainly seems to be due to his cunning with words. His depressing speech to Éowyn in the movie is actually Gandalf’s description of her in the book, but we do get some other examples of Gríma swaying people with words, and even an almost-complimentary response from Gandalf when he calls him ‘bold and cunning… he plays a game with peril and wins a throw.’
So the name Wormtongue is well earned. Keep in mind that a ‘worm’ doesn’t have to be an earthworm, tapeworm, or anything else we call a ‘worm’ in modern English. Historically any narrow creeping or crawling animal (snakes, slugs, caterpillars) could be termed a ‘worm’. In legend and Tolkien, it’s used for dragons, too, and Smaug certainly had a gift of cunning speech. Here, though, I think the reference is more likely to be to a snake; Gandalf calls Gríma a snake more than once. So ‘Snaketongue’, or maybe ‘Dragontongue’, is perhaps a less ‘Evildude’ rendering of the nickname.
But with all that said… the name Gríma itself is not very positive. Like other examples of the Rohirric language, it’s a real word borrowed from Old English. It means ‘mask’ or ‘secret’, also ‘spectre’, and most positively ‘helmet’ (but we know Helm was a Rohirric name with positive connotations, and it seems unlikely that Gríma would be treated as a synonym). It gets even worse when we consider his father’s name, Gálmód, meaning ‘wanton’! (So bad, in fact, that I’ve encountered the theory that it wasn’t really his father’s name, and that ‘son of Gálmód’ was an insult Gandalf made up.)
And this is all in keeping with Gríma’s likely inspiration in the character of Unferth, from Beowulf, whose name Tolkien interpreted as ‘un-peace’ or ‘quarrel’. A sly advisor to the king, opposing the hero(es), bearing an unflattering name? Sounds familiar…