Inteins are named after the organism and gene in which they are found. The organism name follows the same consensus as restriction enzymes and uses a 3 letter genus + species designation, followed by a strain designation, if necessary. The organism name is followed by an abbreviation of the extein name. If more than 1 intein is present in an extein gene, the inteins are given a numerical suffix starting from 5' to 3' or in order of their identification.

For example, the Pyrococcus furiosus ribonucleoside-diphosphate reductase alpha subunit gene contains 2 inteins. The organism is abbreviated as 'Pfu'. Since the gene has been called the 'RIR1' gene, the inteins are named using this gene name. Thus, these 2 inteins are called the Pfu RIR1-1 intein inserted after Gly 301 in the Pfu RIR1 precursor protein and the Pfu RIR1-2 intein inserted after Pro914 in the Pfu RIR1 precursor protein.

Note that an intein name, such as the Pfu RIR1-1 intein, refers to both the intein gene and the intein protein. In many publications, the consensus is to italicize the gene name and to capitalize the first letter of the protein name.
As described below, some inteins are bifunctional proteins that also have endonuclease activity. When endonuclease activity has been demonstrated, the intein is also given a second name that follows the endonuclease naming conventions (Belfort 1997). This name includes the prefix 'PI-', the 3 letter organism abbreviation and a Roman numeral indicating the order of identification of the intein endonuclease in that organism. The endonuclease names for the Pfu RIR1- and Pfu RIR1-2 inteins are PI-PfuI and PI-PfuII, respectively.

There is also a convention for numbering amino acids in inteins. Although we often number the residues in the precursor as a single protein, as when intein insertion site locations are given, a second numbering scheme is often used to assist thinking about inteins in heterologous or foreign exteins. The intein amino acids are numbered from N-terminal to C-terminal beginning with the first residue of the intein and ending with the last residue of the intein. The amino acids in the N-extein: (a) start with the number 1, (b) include a minus sign prefix and (c) are counted from right to left (beginning with the last N-extein residue and going towards the N-terminus). The amino acid preceding the intein is the -1 amino acid. The amino acids in the C-extein: (a) are numbered beginning at the C-terminal splice junction, (b) include a plus sign prefix and (c) are counted from amino to C-terminus.

The first residue following the intein is the mechanistically essential +1 amino acid, which is not technically part of the intein since the intein is defined as the intervening sequence that is spliced out of the precursor.

(Perler, F. B. (2002). InBase, the Intein Database. Nucleic Acids Res. 30, 383-384)