Pass arguments to IDesignTimeDbContextFactory of EF Core

.NET 5 releases in a couple weeks from the time of this answer. So this is possible to change.

Answer Now

The .NET 5, and the associated EF Core 5+ NuGets support this. In Package Manager you can type:

Add-Migration YourMigrationName -Args "Space Separated Args"
Update-Database -Args "Space Separated Args"

For example, I use this:

Update-Database -Args MyConnName

In my Startup project I have a config file (Or appsettings.json) that has that connection string key, and I pull that in.

Note I said .NET Core 5. This will be have a full release in a few weeks from now. So in a few weeks this answer may be simple. But until then, you may need to install Preview versions (And NuGet PreReleases)

Answer Prior to now

There were lacking options when this question was asked, though there were options, like using dotnet ef commands with AppArgs, as discussed here. But these have changed, and are also now accessible from PM Console as discussed in the above "Now" answer.