There’s a department at my workplace where this is common practice too. My old department worked with clients in similar ways, and I was half expecting we’d also be required to do it, but luckily that never happened. Further proof that, at this (generally progressive, flexible-working) company, your actual work-life balance heavily depends who manages you.
As to who you choose, you might consider listing a coworker, your supervisor, or an on-call number if available. Just make sure to clear this with whomever you pick as a support person so they’re aware they’re backing up your calls and emails for emergent situations.

Some of my coworkers have started putting “Thank you for your email” at the beginning of their out of office replies. Management loves it, but I think it’s too ingratiating and I cringe when I read it. These are junior-level staffers, so maybe it makes sense in that context? Anyway, I refuse to put that in my out of office messages.
In the Message and Language section, select the language and enter text, images, and hyperlinks into the Message field. For instructions on language and the use of snippets, click here. Pro Tip: Within the message body, we recommend that you don't use phrases such as: "We are currently out of the office" or "Our office hours are....." Instead, use generic phrases such as "We have received your message and will be in touch." This approach protects your SLA in marketplaces that use detectors to discourage automated responses, which look for these key phrases and may not approve the message as a valid response to reset the SLA.