Putting letters into a garter stitch pattern?

My brother-in-law wants a scarf with his name on it. I’ve already done a gauge swatch, and have the number of sts/rows I need, but he also wants his name on it. How can I put his name into the garter pattern?

Do I just switch to stockinette stitch for the lettering? I’m trying to do this without changing colors, as it’s already going to be a striped scarf.

I made my own lettering chart in photoshop with a 1x1 grid, hopefully that’s also a good way to go at it.

You may be able to use duplicate stitch like this on garter stitch. An alternative might be a stripe at one or both ends in stockinette with the name in purl bumps. I think it’s worth playing around to see what method looks best to you.