I'd think carefully whether you really want to completely cover it. You might be better off in the long run having something a bit more manageable that won't get out of control. Fast-growing climbers tend not to stop at the top of the wall, they move on to invade your roof, and now you are up on a tall ladder dealing with then every year, perhaps more than once a year. But something that stays lower down will still break up the stark lines of the house, and the bare wall above it, now it is no longer so square, sets it off and complements it.

The question "how do I get rid of the ivy which is destroying my house" is a common one on this forum. Russian vine, that's another.

Nick's suggestions are practical, and consistent with my thoughts. But really we need to know the conditions. Clematis are popular climbers, though they tend to reduce to very little during the winter - apart from the few evergreen ones like Armandii suggested by Nick, but they do need t obe well shaded at the base. I plant a bush in front of mine. I also grow clematis tangutica, which has fluffy seedheads which persist through the winter, before you prune it back to almost nothing in Feb. You can grow climbing roses, honeysuckle, even pyracantha (normally a bush), but these need supports, and often a fair bit of sun, though some roses will take part sun. There are climbing hydrangeas which will be happy in a less sunny location. Chocolate vine will be evergreen in a mild location. Jasmine is easy to grow. In asunny spot, with moist soil (if you are so lucky) star jasmine (trachelospermum) will be rather slower, but has an amazing scent. Etc.