Early June: Do we need dining reservations in Murren?

Definitely don't need them for lunch and they'd look at you like you had 3 heads if you tried. Dinner it doesn't hurt to do your most important ones since you have a larger group, but you don't have to do it months or even weeks in advance.

As a courtesy to the restaurant I would suggest definitely making dinner reservations since you are a larger group. You may be able to make a reservation at lunchtime even for that evening.

I strongly suggest you make bookings, at least a few days in advance if you want a popular spot. I was in Brienz last May and all the good restaurants were usually full for dinner, even on weekdays.