“When’s the big day?’’ “Is it a boy or a girl?’’ “Do you have any names picked out?’’

This is the typical flurry of questions that follow the announcement: “We’re having a baby!’’

But for Martin and Michelle Ervin of Hull, the reaction was a little different.

Although they did receive congratulations, one of the first follow-up questions was: “Well, what about the brand?’’

That’s because for the past several years, the couple has been building up a family business, playfully called 9 Lazy Kidz, that features gourmet, all-natural hot sauces — a planned line of nine in total, each one named for, and based on the personalities of, the Ervins’ nine children.

So a 10th child — although an exciting and welcome addition to the family — has created quite the business quandary.

“This started out as a hobby,’’ said Ervin, director of operations for the Boston law firm Prince Lobel Tye LLP. “I did it as a platform to share stories about my kids. I enjoy it; the kids enjoy it. What’s exciting for us now is the new baby, how that impacts the brand, and building momentum around the brand. To me, it’s a great story.’’

Helping them in that quest for brand identity, the family will be the subject of a case study at Bentley University this fall. Because they don’t want students to be influenced before the project begins, professors have asked that the specific details be kept confidential.

However, as Ervin explained, it will be a comprehensive process, with students “doing everything’’ related to the brand, “soup to nuts, top to bottom.’’

Speaking of which, an introduction is in order. The “kidz’’ range in age from 25-year-old Aisha (pronounced “Asia’’) to infant Reign Prince Ervin, born on June 22, at a healthy 10 pounds, 5 ounces. In between (and in descending order) are Tiara, Ramon, Martin Jr., Skye, Myles, Quintin, Malik, and Chance.

So far, the family has released four hot sauces based around them — “Aisha’s Entitlement,’’ “Chance’s Ugh Garlic Sauce,’’ “Q’s Spicy Mango Sauce,’’ and “Skye’s Sweet Apple Heat.’’ Although the couple aren’t doing much to promote or evolve the brand, the sauces can still be purchased online, at www.9lazykidz.com. Ervin estimates that they’ve sold about 7,000 so far, at local retailers, fairs, festivals, and events, as well as through their website.

The upcoming Bentley case study isn’t the first time the family has sought help wrangling the brand. Last year, they took part in the Ad Club’s Brand-a-thon, during which they were paired up with Salem, N.H.-based marketing agency 36 Creative.

Over a 72-hour weekend, the firm strategized and ended up suggesting a change to the name “Nine Lazy Kids’’ (no numeral or “z’’), simplifying the busy colorful labels, and switching the design scheme from actual photos of the children on their namesake sauce to more timeless illustrations.

“There was so much playfulness that they lost some of that established feel, that feeling of trust and honesty,’’ said Trent Sanders, managing partner of 36 Creative. He reflected that “their family is just amazing — there’s some system to the madness.’’

Considering the recent developments — and expansion — in the family, the Ervins haven’t yet put those suggestions into practice. They’re waiting on the Bentley research to make their next strategic move.

As for Sanders’s thoughts on changing the name altogether? “It is tempting to ask the question,’’ he said, suggesting that, in lieu of a name change, the story behind the brand can be told differently. “It’s all about telling the story and how you do it as a brand.’’

In the meantime, Ervin has taken more than a month off from work, allowing his wife to focus her full attention on the baby, while he’s temporarily assumed the day-to-day duties of the seven “kidz’’ still at home (wake-up calls, chores, food preparation, chauffeuring).

“I’m enjoying being a dad for the time that I have. I’m trying to make the most out of it,’’ he said. “I’ve been very fortunate that I get to be part of these 10 kids’ lives.’’

And what about the possibility of 11 Lazy Kidz?

Ervin answered without hesitation: “This is definitely the last. There will be no 11th. I don’t think I have it in me.’’

He quickly added with a laugh: “And Michelle doesn’t either.’’

Taryn Plumb can be reached at tarynplumb1@gmail.com.