1) I'm glad they didn't pick those names. ( When you use did in questions or didn't in negative sentences, you have to take -ed from verbs, for example 'I played football yesterday', if you ask a question it will be Did you play football yesterday? or negative I didn't play football yesterday. Maybe you can practice something here http://learnenglish.britishcouncil.org/en/grammar-exercises, exercises are easy there in the beginning but there are many sites with harder exercises.)

Basic rule: only one past tense verb for each statement about the past. :) So: "I'm glad they didn't pick that name." (or "those names") "Didn't picked" is not possible in English grammar.

I'd like to add one more rule for modal usage in grammar: When using modals, in this case "did", you always use the base form of the verb. The base form is the infinitive form or dictionary form; generally, think of the base form as the form of the verb without any additions (ie, like, happen, PICK). Going on this rule, "did pick" is correct because we have an AUX + verb combination. To negate it, we simply add "not": "did not pick" = "didn't pick". Now you try: Modal + Verb did + go or goes (did go = She didn't go to the store.) will + stays or stay (will stay = The boys will stay with me tonight.) can + balance or balanced (can balance = Both of my cats can balance on a ball.) I hope this helps a bit more on how to use modals with verbs. There's more to modals than just this, of course. But the above should help! Good luck!

the first 1 ) I'm glad they didn't pick that names.