How can I fill the gap?
If I were to choose a one-word expression, that would be a na-adjective 普通【ふつう】.
あなたの 名前【なまえ】は 普通【ふつう】ですか？
However the sentence above may sound a bit rude because it sounds like you are talking whether a name is normal or abnormal, rather than common or uncommon.
(EDIT: There is another na-adjective 一般的【いっぱんてき】, which may be more difficult but safer. "あなたの名前は一般的ですか？")
Alternatively, you can say something like this:
あなたの 名前【なまえ】は よく ある 名前ですか？
(lit. "Is your name a name that exists often?")
あなたの 名前【なまえ】は よく 見【み】る 名前ですか？
(lit. "Is your name a name that you see often?")
Technically speaking, this よくある is a relative clause that modifies 名前 right after it, but you may regard it as a set phrase that just means "common". For example, "Frequently Asked Question" is often translated as "よくある質問【しつもん】" in Japanese.