Mortgage (Joint OR Single)

Two years ago (when I was single) I got a mortgage of 170,000 euro.
Last year I got married and the mortgage remained within my name only.

Are there any benefits from changing this mortgage to a joint mortgage (with my wifes name) OR should I just leave things as they currently are?

I don't think so. See here:

Adding spouse to your mortgage

But make sure to claim the married rate of owner occupier mortgage interest relief.