punctuation - How to punctuate an example indicated by "say"

I'm wondering how commas should be placed around the word "say" and the following clause in a sentence like this:

If you have, say, a bucket, that you would like to fill with water, then ...

This is how I speak the sentence, with minor beaks at ever comma. But it looks odd in text. I've seen others use punctuation in other seemingly random configurations, including with no commas at all, which looks even worse.

One of the reasons I can't work it out is that the bucket here appears to be acting like the subject, and a separate clause (although one that can't be removed without breaking the sentence).

Is there a "best" choice of punctuation for a sentence like this? And is there a name for this kind of built-in-example-clause-thingy?

Answer

It should be punctuated as in your example, with commas around the 'say'.

They are parenthetical commas, because they perform the same function as putting brackets around 'say' - "If you have (say) a bucket..." They are there to prevent the problem you correctly identified, by indicating that 'bucket' is not the object of 'say'.