I quite like it, but then I don't mind surnames as names. Having spent some time living in North America I've got used to it, quite like Parker or Hudson for example. It seems less acceptable in the UK for some reason. If you like it go for it.
You might find it shortened to Spence if that bothers you. Oh and there's a Spencer in Made in Chelsea who seems somewhat of a ladies man, but I don't think that's a reason to avoid.