I received a list (XML) of SRSes by request:
http://gis1:8080/geoserver/wms?SERVICE=WMS&VERSION=1.1.1&REQUEST=GetCapabilities
then parse it and get a list of EPSG codes like "EPSG:1234"
How I can now get a name of specific SRS like "Pulkovo 1942 / Gauss-Kruger zone 13" for "EPSG:28413"?
...or may be I can do it by OpenLayers API?
OGC services do not provide such facilities, they are built under the assumption that you have a EPSG database already available in the client. You can try using some free online service to get to a name (with the perils of a service that is not guaranteed to be available 24x7 of course), like:
A better solution production wise, if you are using GeoServer, is probably to create a WPS process in GeoServer that would do the same job (or create a REST service of your own based on other open source libraries).