If someone doesn't like fish, kangaroos or zebras then they won't check out your shop.
Bree's or Breeze Baby Quilts says it all now. If in the future you might expand then maybe just Bree's quilts and more.

What about "Brees's Baby Quilts". I also agree, you need the word quilts in the name.

Easy Breezy Quilts, Easy Breezy Baby Quilts. Easy Breezy Patchwork Place. I like rhymes, easy to remember.

Ahoy about "Babysoft Quilts" ? Short, catchy, easy to remember.....

What about Little Bree Quilts?

You've received some great responses, so I won't throw another name in the pot. My advice, though, is to leave enough space for growth in your quilting interests. There are aspects of quilting that I said I'd NEVER delve into; crazy quilting being one of them. Guess who's a crazy quilter today, among other things? I am. You may branch out to do other things; so I'd select a name that gives you room to grow, if you will. Don't completely box yourself in. If you're starting a business, you don't ever want to have to redo your name. Once you've got business cards, brochures, website, email -- whatever -- let it done; with no regrets later on down the road.

Hope this was helpful.

Good question - I'd first check to see what's taken. Then consider what you really like, fabric, stitching, time with family/friends, and work it in.

I'm immediately drawn to the kangaroo one it sounds "baby" to me & the 2 tier name is a really good idea- Unique Baby Items would allow you to branch out- or bundle items into layette sets. By the way starting your name with the article "a" won't put you at or near the top of a search list (paying Google will however...) -search engines ignore "the,a
& an".