Since other people are posting minor variations of existing answers, here is my take which is a combination of two previous answers:
& coding challenges
First of all, I think @ais523_permanent_community_wiki's suggestion of using a subtitle is great. We emphasize the term 'Code Golf' as our main title, and add a relevant sub-title below it. His answer already explains the reasoning behind it, which I can only agree with (and given the amount of upvotes on his answer, others agree with as well).
Second, I think we should get rid of the term 'programming', so new users are less likely to come to us thinking it's a Q&A. Although I've seen some answers use the term '& coding contests', I personally prefer @ConorO'Brien's answer with 'Code Golf & challenges.
The term 'challenges' is already a commonly accepted term in the PPCG community. When new users post a question that would belong on StackOverflow, we explain that PPCG is about programming challenges and we direct them to SO. When a new user posts a challenge that can be perfected, we direct them to the Sandbox of Proposed Challenges. When we search for the term 'challenge' we -currently- get 165 pages of results, whereas with the term 'contest' we -currently- only get 11 pages of results. The only time I hear the term 'contest' is with popularity-contest challenges, which are rather off-topic in our current meta (unless it's a cops-and-robbers challenge). If we look at the newest [popularity-contest] challenges and select the first which isn't [cops-and-robbers] nor [closed], it would be this one from the start of 2018.
So, although 'contests' isn't a bad term either, my preference would go to 'challenges' since it's already a commonly accepted term within our community.
EDIT: In addition, as correctly pointed out by @trichoplax in the comments below. The term 'contests' suggest a ranked system and a competition. Whereas the term 'challenge' suggests something to achieve. Although they are rather similar, I see one key differences: in 'contests' people compete against each other; whereas in 'challenges' one (or multiple people with each other) accomplishes an achievement.
If we were really competing against each other, people would also rather post a shorter answer themselves in the same language, instead of suggesting a golf on an existing answer.
I personally do these code-golf challenges for my own enjoyment, and whether I have the shortest answer in an 05AB1E answer, or the longest answer in a Java answer is irrelevant. Which is why, in combination that it already is a pretty common term within our community, I prefer the term 'challenges' over 'contests'.
EDIT 2: I will also quote's @Catija♦'s comment, with the preference of 'coding challenges' as well from a non-programming point of view:
Since you ask, my personal preference of the ones I've seen so far is to use "& coding challenges". It's not really long, which is nice. For me, "contests" implies a prize... you enter a contest to win something and here, all you're getting is votes. When we have a "contest" on the network, that's usually coupled with some physical prize, so "contests" seems like the wrong message. The real content here (from what I see) are challenges - even code golfing itself is a challenge - where the goal is to make the code as short as possible.
Come for the code stay for the Dennis.- The subtext could be a slogan instead of an extension of "Code Golf". \$\endgroup\$
(Not Stack Overflow). \$\endgroup\$