Basemaps obtained through the QuickMapServices plugin are WMS (Web Map Service) layers. With a WMS layer, what you see is what you get. You don't have any control over individual labels and features.
A WFS (Web Feature Service) layer, on the other hand, allows you to access and manipulate features and labels through queries. See this page for more info on the difference between WMS and WFS layers.
In order to control individual labels, you need the data either as a vector layer, or as a WFS layer.
The national map viewer provides several WFS layers. Transportation, govunits and geonames are probably the ones you want. See QGIS Training Manual, 11.2. Lesson: Web Feature Services for instructions on adding a WFS layer.
Or you can download individual features (such as sections of I-90 in North Dakota) from Open Street Map with the QuickOSM or OSMDownloader plugin.
Here's an example of how to download and label I-90 in South Dakota using the QuickOSM plugin:
Zoom to South Dakota on your map canvas. Open QuickOSM.
Key: highway; Value: motorway; choose "Extent of the map canvas"
Alternatively, draw a polygon around your area of interest and use the extent of that layer instead of the extent of the canvas.
After running that query, you should have a layer of points and one of lines. Here's what the lines layer looks like:
Important: This is a temporary layer. Temporary layers are deleted as soon as you close the project. Be sure to export it to a permanent file before proceeding. Right click on the layer name > export > save features as...
By using the Identify tool, we can see that the name of the highway is stored in a field called "tiger:name_base".
Now we can set up a rule-based label so that only the I-90 highway portions are labeled.
Open layer styling > labels. Select rule-based labels. Type in a filter expression:
"tiger:name_base" = 'I-90'
"tiger:name_base" in the text box next to "Label with".
Here's what the labels look like now:
One of the best features of QGIS is layer styling and labeling. You really have a lot of control over how your features are displayed and labeled. See QGIS Training Manual, 4.2. Lesson: The Label Tool for more information on customizing labels.
To add labels for towns along I-90, decide how wide an area you want to include. Buffer the I-90 highway line by that amount. Use the buffer as the extent for a QuickOSM query of cities, towns, villages etc.