My wifes daughter would like to change her surname to mine,she's lived with us for 14 year and is now 24 year old. How do we go about it?

She can ask the amphur, but a Thai must have a THai name that has a meaning in Thai. Your wife can take your name, but her daughter is not related to you. So formally they should refuse the request.

In practise they might allow it, depending on the amphur. But probably they will tell her to get adopted by you so she can change her name.