According to the pension index by regiment:
in co.A, 2 of 132 men who received pensions enlisted under aliases
in co.B, 7 of 122 men who received pensions enlisted under aliases
If this sample is representative, 3.5% of the men in the regiment (about 70 total) had aliases.
This may underestimate the number of aliases. According to the 1890 census, John Legg enlisted under the alias 'John Lackey'. He did apply for a pension, but the pension index by regiment does not mention his alias. Louis F Hohl also enlisted under an alias without the pension index cards mentioning it.
After the war, enough men had difficulties (especially gaining pensions) because they had served under aliases that in 1890 Congress required the Secretaries of War and the Navy to issue revised discharges in the man's true name.