I believe what you are referring to is the "Remember search and form history" preference in your browser. It is not specific to Family Echo. You can turn it off in your browser under Tools, Options, Privacy...but I don't know of any way to adjust it to what you're asking for.
If you are working in different trees, you could log in once on Firefox and once on Google Chrome and then your form history would be separate that way. You can also remove individual form history by down-arrowing to one you want to remove and hitting the Delete key. I do this when I've moved on from say, a family who was all born in Pennsylvania, and now I'm onto families all born in Illinois. I just Delete the Pennsylvania results but don't turn off my form history, because then I would lose all the last names I want to retain.
Lastly, a word of warning - depending on your Clear Recent History settings, form history will be removed every time you clear your cookies. I've kicked myself after clearing cookies out of habit and realizing my suggested names/form history have disappeared, as well. To avoid this, just click History, Clear Recent History, and uncheck the Form & Search History option.