You can set up a custom BLAST database using sequences you already have in your Geneious database, or from a FASTA file of sequences you have downloaded from elsewhere. You first need to set up the custom BLAST service under Tools→Add/Remove Databases→Set up Search Services. To create the custom database use Tools→Add/Remove Databases→Add Sequence Database. The Geneious User Manual has more detailed information on how to set this up.
Note, if you wish to create pre-formatted BLAST databases from fasta files outside of Geneious, you can also run the BLAST+ executables from the command line using the makeblastdb command. Then put the formatted BLAST database files which are created (there will be multiple files per database) in the BLAST/data folder that was created in your Geneious Data folder when you set up custom BLAST, restart Geneious and the new database will show up when you run custom BLAST. However, if the database is formatted manually using makeblastdb, there will be no annotations on the resulting alignments. If it is formatted from within Geneious, then an extra file is created with the annotations so Geneious can put them back onto the alignments after a search.