Its better to keep the ' Tech domain Owner' as a reference field. Because what if there are two 2 people with the same name? Always better to point the record in user table.

For approvals, you can use approval user activity,

and add an advanced script - 

answer=[];

answer.push(current.variables.<back-end name of tech domain owner field>); ---> This is the sys_id that you are pushing.

If you are not changing the field to reference, then, you need to do a Gliderecord to user table with user's name first and get the sys_id which you can pass here. But again, that is not a very good idea.

Give it a try.