I tried to create a signature with the information I wished to convey:
I found I wasn’t able to do this.
Please add an “Organization” field to the signature block.
Alternatively, you could make the signature block just a free-form text field and allow people to put whatever they want.
I had a similar issue, and ended up using the option to write your own HTML signature block (labelled “Raw HTML” at the far right of the selection of predefined styles). It will give the the HTML for the current state of the sig, so you can set most up as you want using the form and then edit the HTML. (You can also just enter plain text, if you’re not the sort of person who writes HTML, although you won’t get any formatting in that case.)
I agree, though, that an Organisation block would seem obvious for business use of the software. For the moment, I entered my job title and business into the Title field!