You are right- in the Bible the God is treated many times in plural, mainly אלוהים & אדוני.
Those names (in plural) are used also in spoken language.
Apart of those two I don't remember other options, and all the verbs and adjectives related to them are in singular.
I am not sure I understood your question: what has the word מחמדים to do with the God?
I don't remember it as one of his (many) names.
The singular of מחמדים is מחמד as you said, this is a very literary word, so you might find it in expressions, verses from the Bible, etc.