The very fact you have to deter people from mentioning 'jail' tells me that you have heard this more than you would like....ummm.....there's your answer....the name stirs up something other than what you intend.
Honestly, the name 'The Framed Life' does not make me think of photography in any way. If you walked up with a camera and said 'I'm from The Framed Life' I would instantly think paparazzi or something like that. It just doesn't have a positive connotation, in my opinion.
If you owned a custom framing shop....that name would certainly work.
As for the logo, the square looks more like an Aspen leaf than a 'frame'. Again, just my opinion. But I look at the logo and I do not think photography. Being a photographer, if I don't get it, then the general public is even less likely to get it.
Here is what I have been told by marketing people. Your business, especially a service business, should either include your name (for name branding) or state what you do. For example, Peak Photography or Johnson Portrait Photography. There is no confusion for the general public. We, as professionals, often tend to want to be overly creative and all though our colleagues might understand a name like 'Captured by Aperture', the general public just doesn't get it.
A couple suggestions that come to mind are: 'Life Framed' by James Robertson and 'Framed Memories'
For some reason, I just like the sound of 'Life Framed' better than 'The Framed Life'.
I just asked my wife real quick what she thought and she said she wouldn't connect 'The Framed Life' with photography either....and she's married to a photographer. I think you can play around with the words....maybe even 'Life....Framed' or 'Life, Framed'. Hmmm.....maybe a 'Life Framed' on top and 'Photography' underneath it in smaller font but stretched.
Anyway, I'm certainly not bashing you or your idea, just giving my opinion. Hopefully I didn't write anything that comes across the right way.