They have several of them...the cross, or crucifix is just the most popular.The symbol of Christian religion is Cross.
Symbols are interesting things...they mean more'n what the user tells us they mean. No matter how Xtians try to slice it, their use of symbols is rooted in primitive mans oldest beliefs that use mandalas, icons and other such things to ward off, or bring forth spiritual energies thought to originate from their God/s.
Is the fish an old pagan image? Yes. Is its use in Xtian history mean the same things? No. But there are others they use where they do borrow ideas and beliefs to their own advantage. Be they the notion of the Sun Gods, or the Underworlds of most cultures myths - or the good old flood story. Judeo-Xtianity and its red-headed step child Islam - all borrow from and co-opt old pagan and non-pagan spiritual ideas, icons, imagery, sub-text, etc, etc...
Its a given. As to what they mean to Xtians, the Jews and Muslims - that's a whole other discussion. But to deny them straight out and claim them as original to their beliefs system is absurd, and an epic failure of reasoning.
Plus, Xtianity and Xtians in this case here - can not control what their symbols mean to others. No way! When I see a cross or a crucifix now, I see nothing but death and destruction within the Belief System. I see that punishment-torture device as the complete opposite of what the teachings of and the teacher himself would have wanted as a Brand.
I see it as the symbol of a Death Cult. One fixated on an afterlife - often at the cost of other lives for the one we can actually know and live. I see none of the love and compassion of the man nailed to it that some Xtians try to peddle...I see none of that. I see a man tortured and murdered by his own people for teaching a few unique ideas about ones personal spiritual journey.
I see that his trial and punishment are more worthy of adoration than were his simple teachings. I see that in order to justify his torture and murder as a sacrifice - someone decided to make him a God who died for us. A god in the flesh, who's only destiny was to be murdered. And that his followers would worship that murder over a set of very simple teachings about living alongside others.
But amazingly enough - a lot of people find solace in that imagery of torture and death.
Now the fish, that makes a whole lot more sense to me. Life in the form of its own fish-hood and as sustenance for many creatures on the planet. Part of the good side of the cycle of life. Instead of the awful side that Humans add to it. Torture and murder for having a differing set of ideas about how to live in peace and give a little push-back to those who wish to control others thoughts and beliefs about their spiritual lives.
A fish. Conjures thoughts of a school of fish like humans, a place to feel safe, a food source, water, beauty, life...all positive.
A torture and murder device.(sometimes with a dead "body" on it!) Uh...I'm thinking, I'm thinking...nope. Nothing positive there...nada.