will it be perceived as a weird looking “h”

No, it looks like FI, but you probably ought to move the I a little closer to the F to make the interletter spacing consistent.

I think the lettering is to tight overall. That spacing looks 1970s, let it breathe.

looks a bit too much like the addison logo:

http://www.addison.com/

firefish is a name with lots of visual connotations, why not investigate those more?

kerning is unbalanced, especially since you are using a ligature, which pretty much sets the spacing for the rest of the letters.

Icon needs to be bigger. I can't tell what it is.