Baby Gifts Pouring in for Jennifer Lopez & Marc Anthony

New parents Jennifer Lopez and Marc Anthony have received multiple deliveries of gifts to their Long Island home for their newborn twins, a source tells PEOPLE.

"The twins already got a ton of embroidered pillows with their names on them," says the source – though Anthony and Lopez have not released the names of their son and daughter, who were born Feb 22.

"Jennifer also is getting baby carriers with the names etched on them by Baby K'tan," adds the source.

A spokesperson for Baby K'tan in Fort Lauderdale confirms that pink and blue embroidery were used respectively on the 100 percent cotton carriers and that they "were purchased from us as gifts for both J.Lo and Marc."

In addition, members of Lopez's family were spotted shopping at Baby Gap in Americana Manhasset mall last week, confirms a sales rep from the store.

As for how the do mom is doing, Lopez left the hospital this week and "is resting comfortably at home," according to close friend.

Re: Baby Gifts Pouring in for Jennifer Lopez & Marc Anthony

I'm so glad they're getting gifts. I can't imagine how they'd ever get by without the generosity of others!

Re: Baby Gifts Pouring in for Jennifer Lopez & Marc Anthony

So how come we haven't heard their names leaked like these other details? I mean, people who did the embroidery know the names!