|Load your verbs into a collection - an array or list, whichever you want.
Do the same with the adjectives
Then create another collection which takes two indexes into the collections: that stores the "used" tags so you don't repeat. A Dictionary<int, int> should do it. Load it with the gamertags that you've actually issued.
Now, to generate a new tag, pick two indexes at random. Check to see if they are already used together. If they aren't, add them, and you have your tag.
If not, generate two more and try again.
Think of it as if you were doing it with a paper and pencil, and you'll see what I mean.
There are more efficient ways (ensuring you can't generate duplicates instead of checking for them) but they are rather more complicated, particularly for a beginner.
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