The case of śrī is similar, although it is definitely more common as a prefix.
My impression is that ārya is more common as a prefix, especially in Classical Sanskrit (e.g., ārya cāṇakya in the play Mudrā-rākṣasa). Its being an address or attention-calling term (functionally, not semantically) like he, bhoḥ etc. also makes it natural that it should occur as a prefix (āryehīty upaguhya occurs in verse 4 of Samudra-gupta’s Allahabad inscription). I also recall that texts on dramaturgy, poetics etc. prescribe that ārya, among other words, is to be used as an address term.
The use of ārya as a suffix may have been more common in referring to women, since its Pkt and later derivates (ajjā, ā.ī etc.) seem to occur after female names, unless the use of ayyā at the end of male names occurring in South Indian languages is related to ārya. Female deity names may also have been exceptional as in Āryāmbikā.
a.a.
One occasionally comes across ārya in Sanskrit texts either
suffixed to a name (e.g., Rāmānujārya) or prefixed to it (e.g.,
Āryāvalokiteśvara), but I haven't seen this often enough to be
certain if either variant is peculiar to a particular region,
religious community, etc. … As a result, I am uncertain how to
understand the occasional ārya in a compounded list of
names. … whether it is more usual as a prefix or suffix, or under what
circumstances this might vary.