Cut the soil with 50% perlite, for an easy fix to your soil problem. Attempt to grow it horizontally, if you've got a pot that would accommodate that - this plant's preference is to grow that way.

Looks like Echeveria Perle von Nurnberg (need front view). They will grow tall trunks; definitely change potting mix, it is too wet.

Only way to 'change' it is to behead it - cut off top rosette, let callus and pot into grittier mix. You could leave original stalk potted as it likely will grow few babies too.

The new plant will grow similar, but it will be a while before you need to do it again.

Here is one that was cut off about week - 10 days ago, new branches are starting to grow - sorry it's such a blurry photo...

Ah thank you both! Yes it's going into some decent compost mix asap, I was all out and made do with a gritty mix.

I'm really sorry but when you say grow it horizontally, do you mean literally let it flop over and grow that way? I'm sure I could find a spot for it.

I had thought of the decapitation method but didn't know if that was ok!

Thanks for the advice - basically, if it's not a flowering cactus I have no idea what to do!

P.s. thanks for the ident, she is a pretty one:

Katie

It is succulent, not cacti :) (all cacti are succulents, but not all succulents are cacti).

I never grew one horizontally - at least not on purpose, but had one leaning quite a bit, here she is:

Bottom of trunk/roots are in red pot on very left, plant just leaning to the right...I eventually beheaded it.