Who do we call to have drainage problems in our yard fixed.

You need to have the yard regraded, possibly some drains to divert the water to disburse it more evenly. You need a landscape architect.

I would call the City Building Inspector. He can come take a look and advise you as to steps needed and where/who to contact

A good landscaper can do this. Look at the possibly of putting a burm at the street to stop it or divert it before it coming in your yard.

I would put in a french drain to move that water out to the curb and storm drain. Be sure to have utility company come out and mark utilities first, usually free of charge.

https://www.youtube.com/watch?v=9RQYN9fRcc8

https://www.youtube.com/watch?v=XDOUmX1meAs

https://www.youtube.com/watch?v=XmmdGiEh1Mw&t=285s

You need a plumber and a landscape engineer. A sump pump and a French drain may both be needed. And if your uphill neighbors' runoff is coming into your yard, you need a retaining wall of concrete blocks at the top of your yard. You can make calls to at least three city departments (sewer, water reclamation/recycling, code enforcement, land use, planning, etc) to see if you can get any advice or plans or even financial assistance from the city or county. You will probably need to plant some shrubs or trees with deep roots on the upper part of your land and maybe resod after the rain (and snow) has ended. Best wishes 😇💞.

if you can't move the water to the gutter, try adding a dry well. i'm putting one in this fall using an old 32 gallon trash can i don't need. you can always add them in a chain if necessary. lots of videos on YouTube and pinterest. 8^)