How do jokes with "だけに" work?

Question

There's a particular style of joke/pun in Japanese that I'm not sure how to describe, so let me provide some examples:

カミングスーン、神だけに。

(said by someone who has recently become a 神)

バスケットだけに助っ人募集中。

(said by someone who is looking for people to help out a basketball team)

A: それに、学校の皆に会えば、キャッチフレーズが思いつきそうだなあって。
B: 思いつく？
C: お餅つきだけに！

(following a conversation about giving mochi to classmates and trying to come up with a catchphrase)

---

Now that we've established what I'm talking about, my questions are as follows:

1. Is there a name for these jokes? (Would you just call them ダジャレ?)

2. What is going on grammatically in these jokes? This doesn't seem to be one of the simple/compositional usages of だけ＋に found e.g. here at dictionary.goo.ne.jp.

3. Is there a rough English equivalent of these jokes? I've seen translations that basically introduce a pun related to the topic of the joke and then append "No pun intended", presumably corresponding to the だけに part. Of course, joke translation is a peril-fraught thing, so I'm not placing too much stock in this.

Answer 1

1. This kind of (rather poor) pun is generally considered to be おやじギャグ. As far as I know, there is no word specifically referring to "AだけにB" jokes.

2. I think the third meaning of that dictionary (であるから、それにふさわしく) can be applied. 「バスケット, therefore I say, スケット」.

3. Sorry, I'm not the right person to answer this part of your question. However, "no pun intended" seems to be very loose translation, because a pun is certainly intended when you use "だけに" in this way.