SEATTLE — For almost 50 years, Washington has written billions of dollars in financial-aid checks to Washington college students through a program with a most uninspiring name: the State Need Grant. Now Gov. Jay Inslee wants to give the program a big boost in funding, and to rename it with a sunnier moniker. The budget proposal, which would provide an additional $103 million for the program in 2019-21, would guarantee that by 2021-22, the estimated 93,000 students whose families make 70 percent or less of the state’s median family income will get help paying for college (in 2018-19, that was an adjusted gross income plus nontaxable income of $61,500 for a family of four).